diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/1024.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/1024.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c1930055474071e7a05126f1643941c601bb096d
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/1024.txt
@@ -0,0 +1,347 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ \frac{12}{7} & 2 \\
+ -\frac{1}{7} & -\frac{10}{7} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ \frac{16}{7} & \frac{3}{7} & \frac{15}{7} \\
+ -2 & \frac{3}{7} & \frac{9}{7} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ \frac{12}{7} & 2 \\
+ -\frac{1}{7} & -\frac{10}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{16}{7} & \frac{3}{7} & \frac{15}{7} \\
+ -2 & \frac{3}{7} & \frac{9}{7} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{12}{7} & 2 \\
+ -\frac{1}{7} & -\frac{10}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{16}{7} & \frac{3}{7} & \frac{15}{7} \\
+ -2 & \frac{3}{7} & \frac{9}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{12}{7} & 2 \\
+ -\frac{1}{7} & -\frac{10}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{16}{7} & \frac{3}{7} & \frac{15}{7} \\
+ -2 & \frac{3}{7} & \frac{9}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{12\ 16}{7\ 7}+2 (-2)=-\frac{4}{49}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{12}{7} & 2 \\
+ -\frac{1}{7} & -\frac{10}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{16}{7} & \frac{3}{7} & \frac{15}{7} \\
+ -2 & \frac{3}{7} & \frac{9}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$-\frac{4}{49}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{12}{7} & 2 \\
+ -\frac{1}{7} & -\frac{10}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{16}{7} & \frac{3}{7} & \frac{15}{7} \\
+ -2 & \frac{3}{7} & \frac{9}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{4}{49} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{12\ 3}{7\ 7}+\frac{2\ 3}{7}=\frac{78}{49}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{12}{7} & 2 \\
+ -\frac{1}{7} & -\frac{10}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{16}{7} & \frac{3}{7} & \frac{15}{7} \\
+ -2 & \frac{3}{7} & \frac{9}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{4}{49} & \fbox{$\frac{78}{49}$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{12}{7} & 2 \\
+ -\frac{1}{7} & -\frac{10}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{16}{7} & \frac{3}{7} & \frac{15}{7} \\
+ -2 & \frac{3}{7} & \frac{9}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{4}{49} & \frac{78}{49} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{12\ 15}{7\ 7}+\frac{2\ 9}{7}=\frac{306}{49}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{12}{7} & 2 \\
+ -\frac{1}{7} & -\frac{10}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{16}{7} & \frac{3}{7} & \frac{15}{7} \\
+ -2 & \frac{3}{7} & \frac{9}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{4}{49} & \frac{78}{49} & \fbox{$\frac{306}{49}$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{12}{7} & 2 \\
+ -\frac{1}{7} & -\frac{10}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{16}{7} & \frac{3}{7} & \frac{15}{7} \\
+ -2 & \frac{3}{7} & \frac{9}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{4}{49} & \frac{78}{49} & \frac{306}{49} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{7} \left(-\frac{16}{7}\right)+\left(-\frac{10}{7}\right)\, (-2)=\frac{124}{49}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{12}{7} & 2 \\
+ -\frac{1}{7} & -\frac{10}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{16}{7} & \frac{3}{7} & \frac{15}{7} \\
+ -2 & \frac{3}{7} & \frac{9}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{4}{49} & \frac{78}{49} & \frac{306}{49} \\
+ \fbox{$\frac{124}{49}$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{12}{7} & 2 \\
+ -\frac{1}{7} & -\frac{10}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{16}{7} & \frac{3}{7} & \frac{15}{7} \\
+ -2 & \frac{3}{7} & \frac{9}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{4}{49} & \frac{78}{49} & \frac{306}{49} \\
+ \frac{124}{49} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{7} \left(-\frac{3}{7}\right)+\left(-\frac{10}{7}\right)\, \times \, \frac{3}{7}=-\frac{33}{49}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{12}{7} & 2 \\
+ -\frac{1}{7} & -\frac{10}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{16}{7} & \frac{3}{7} & \frac{15}{7} \\
+ -2 & \frac{3}{7} & \frac{9}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{4}{49} & \frac{78}{49} & \frac{306}{49} \\
+ \frac{124}{49} & \fbox{$-\frac{33}{49}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{12}{7} & 2 \\
+ -\frac{1}{7} & -\frac{10}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{16}{7} & \frac{3}{7} & \frac{15}{7} \\
+ -2 & \frac{3}{7} & \frac{9}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{4}{49} & \frac{78}{49} & \frac{306}{49} \\
+ \frac{124}{49} & -\frac{33}{49} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{7} \left(-\frac{15}{7}\right)+\left(-\frac{10}{7}\right)\, \times \, \frac{9}{7}=-\frac{15}{7}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ \frac{12}{7} & 2 \\
+ -\frac{1}{7} & -\frac{10}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{16}{7} & \frac{3}{7} & \frac{15}{7} \\
+ -2 & \frac{3}{7} & \frac{9}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{4}{49} & \frac{78}{49} & \frac{306}{49} \\
+ \frac{124}{49} & -\frac{33}{49} & \fbox{$-\frac{15}{7}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/1056.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/1056.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4e87ee8006554265908fe252c7d41170f08e3557
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/1056.txt
@@ -0,0 +1,549 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ -\frac{1}{4} & -\frac{1}{4} & \frac{1}{2} \\
+ -\frac{3}{2} & \frac{1}{4} & \frac{9}{4} \\
+ \frac{3}{2} & -\frac{7}{4} & \frac{9}{4} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ \frac{5}{2} & 1 & \frac{7}{4} \\
+ \frac{1}{4} & \frac{1}{2} & -2 \\
+ -\frac{7}{4} & -1 & 3 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{1}{4} & -\frac{1}{4} & \frac{1}{2} \\
+ -\frac{3}{2} & \frac{1}{4} & \frac{9}{4} \\
+ \frac{3}{2} & -\frac{7}{4} & \frac{9}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{5}{2} & 1 & \frac{7}{4} \\
+ \frac{1}{4} & \frac{1}{2} & -2 \\
+ -\frac{7}{4} & -1 & 3 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{1}{4} & -\frac{1}{4} & \frac{1}{2} \\
+ -\frac{3}{2} & \frac{1}{4} & \frac{9}{4} \\
+ \frac{3}{2} & -\frac{7}{4} & \frac{9}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{5}{2} & 1 & \frac{7}{4} \\
+ \frac{1}{4} & \frac{1}{2} & -2 \\
+ -\frac{7}{4} & -1 & 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{1}{4} & -\frac{1}{4} & \frac{1}{2} \\
+ -\frac{3}{2} & \frac{1}{4} & \frac{9}{4} \\
+ \frac{3}{2} & -\frac{7}{4} & \frac{9}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{5}{2} & 1 & \frac{7}{4} \\
+ \frac{1}{4} & \frac{1}{2} & -2 \\
+ -\frac{7}{4} & -1 & 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{4} \left(-\frac{5}{2}\right)+\frac{1}{4} \left(-\frac{1}{4}\right)-\frac{7}{2\ 4}=-\frac{25}{16}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{1}{4} & -\frac{1}{4} & \frac{1}{2} \\
+ -\frac{3}{2} & \frac{1}{4} & \frac{9}{4} \\
+ \frac{3}{2} & -\frac{7}{4} & \frac{9}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{5}{2} & 1 & \frac{7}{4} \\
+ \frac{1}{4} & \frac{1}{2} & -2 \\
+ -\frac{7}{4} & -1 & 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$-\frac{25}{16}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{1}{4} & -\frac{1}{4} & \frac{1}{2} \\
+ -\frac{3}{2} & \frac{1}{4} & \frac{9}{4} \\
+ \frac{3}{2} & -\frac{7}{4} & \frac{9}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{5}{2} & 1 & \frac{7}{4} \\
+ \frac{1}{4} & \frac{1}{2} & -2 \\
+ -\frac{7}{4} & -1 & 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{25}{16} & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{4} (-1)+\frac{1}{4} \left(-\frac{1}{2}\right)-\frac{1}{2}=-\frac{7}{8}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{1}{4} & -\frac{1}{4} & \frac{1}{2} \\
+ -\frac{3}{2} & \frac{1}{4} & \frac{9}{4} \\
+ \frac{3}{2} & -\frac{7}{4} & \frac{9}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{5}{2} & 1 & \frac{7}{4} \\
+ \frac{1}{4} & \frac{1}{2} & -2 \\
+ -\frac{7}{4} & -1 & 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{25}{16} & \fbox{$-\frac{7}{8}$} & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{1}{4} & -\frac{1}{4} & \frac{1}{2} \\
+ -\frac{3}{2} & \frac{1}{4} & \frac{9}{4} \\
+ \frac{3}{2} & -\frac{7}{4} & \frac{9}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{5}{2} & 1 & \frac{7}{4} \\
+ \frac{1}{4} & \frac{1}{2} & -2 \\
+ -\frac{7}{4} & -1 & 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{25}{16} & -\frac{7}{8} & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{4} \left(-\frac{7}{4}\right)+\frac{2}{4}+\frac{3}{2}=\frac{25}{16}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{1}{4} & -\frac{1}{4} & \frac{1}{2} \\
+ -\frac{3}{2} & \frac{1}{4} & \frac{9}{4} \\
+ \frac{3}{2} & -\frac{7}{4} & \frac{9}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{5}{2} & 1 & \frac{7}{4} \\
+ \frac{1}{4} & \frac{1}{2} & -2 \\
+ -\frac{7}{4} & -1 & 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{25}{16} & -\frac{7}{8} & \fbox{$\frac{25}{16}$} \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{1}{4} & -\frac{1}{4} & \frac{1}{2} \\
+ -\frac{3}{2} & \frac{1}{4} & \frac{9}{4} \\
+ \frac{3}{2} & -\frac{7}{4} & \frac{9}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{5}{2} & 1 & \frac{7}{4} \\
+ \frac{1}{4} & \frac{1}{2} & -2 \\
+ -\frac{7}{4} & -1 & 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{25}{16} & -\frac{7}{8} & \frac{25}{16} \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{3}{2}\right)\, \times \, \frac{5}{2}+\frac{1}{4\ 4}+\frac{9 (-7)}{4\ 4}=-\frac{61}{8}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{1}{4} & -\frac{1}{4} & \frac{1}{2} \\
+ -\frac{3}{2} & \frac{1}{4} & \frac{9}{4} \\
+ \frac{3}{2} & -\frac{7}{4} & \frac{9}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{5}{2} & 1 & \frac{7}{4} \\
+ \frac{1}{4} & \frac{1}{2} & -2 \\
+ -\frac{7}{4} & -1 & 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{25}{16} & -\frac{7}{8} & \frac{25}{16} \\
+ \fbox{$-\frac{61}{8}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{1}{4} & -\frac{1}{4} & \frac{1}{2} \\
+ -\frac{3}{2} & \frac{1}{4} & \frac{9}{4} \\
+ \frac{3}{2} & -\frac{7}{4} & \frac{9}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{5}{2} & 1 & \frac{7}{4} \\
+ \frac{1}{4} & \frac{1}{2} & -2 \\
+ -\frac{7}{4} & -1 & 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{25}{16} & -\frac{7}{8} & \frac{25}{16} \\
+ -\frac{61}{8} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{3}{2}\right)\, \times \, 1+\frac{1}{4\ 2}+\frac{9 (-1)}{4}=-\frac{29}{8}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{1}{4} & -\frac{1}{4} & \frac{1}{2} \\
+ -\frac{3}{2} & \frac{1}{4} & \frac{9}{4} \\
+ \frac{3}{2} & -\frac{7}{4} & \frac{9}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{5}{2} & 1 & \frac{7}{4} \\
+ \frac{1}{4} & \frac{1}{2} & -2 \\
+ -\frac{7}{4} & -1 & 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{25}{16} & -\frac{7}{8} & \frac{25}{16} \\
+ -\frac{61}{8} & \fbox{$-\frac{29}{8}$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{1}{4} & -\frac{1}{4} & \frac{1}{2} \\
+ -\frac{3}{2} & \frac{1}{4} & \frac{9}{4} \\
+ \frac{3}{2} & -\frac{7}{4} & \frac{9}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{5}{2} & 1 & \frac{7}{4} \\
+ \frac{1}{4} & \frac{1}{2} & -2 \\
+ -\frac{7}{4} & -1 & 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{25}{16} & -\frac{7}{8} & \frac{25}{16} \\
+ -\frac{61}{8} & -\frac{29}{8} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{3}{2}\right)\, \times \, \frac{7}{4}-\frac{2}{4}+\frac{9\ 3}{4}=\frac{29}{8}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{1}{4} & -\frac{1}{4} & \frac{1}{2} \\
+ -\frac{3}{2} & \frac{1}{4} & \frac{9}{4} \\
+ \frac{3}{2} & -\frac{7}{4} & \frac{9}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{5}{2} & 1 & \frac{7}{4} \\
+ \frac{1}{4} & \frac{1}{2} & -2 \\
+ -\frac{7}{4} & -1 & 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{25}{16} & -\frac{7}{8} & \frac{25}{16} \\
+ -\frac{61}{8} & -\frac{29}{8} & \fbox{$\frac{29}{8}$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{1}{4} & -\frac{1}{4} & \frac{1}{2} \\
+ -\frac{3}{2} & \frac{1}{4} & \frac{9}{4} \\
+ \frac{3}{2} & -\frac{7}{4} & \frac{9}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{5}{2} & 1 & \frac{7}{4} \\
+ \frac{1}{4} & \frac{1}{2} & -2 \\
+ -\frac{7}{4} & -1 & 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{25}{16} & -\frac{7}{8} & \frac{25}{16} \\
+ -\frac{61}{8} & -\frac{29}{8} & \frac{29}{8} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{3\ 5}{2\ 2}+\left(-\frac{7}{4}\right)\, \times \, \frac{1}{4}+\frac{9 (-7)}{4\ 4}=-\frac{5}{8}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{1}{4} & -\frac{1}{4} & \frac{1}{2} \\
+ -\frac{3}{2} & \frac{1}{4} & \frac{9}{4} \\
+ \frac{3}{2} & -\frac{7}{4} & \frac{9}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{5}{2} & 1 & \frac{7}{4} \\
+ \frac{1}{4} & \frac{1}{2} & -2 \\
+ -\frac{7}{4} & -1 & 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{25}{16} & -\frac{7}{8} & \frac{25}{16} \\
+ -\frac{61}{8} & -\frac{29}{8} & \frac{29}{8} \\
+ \fbox{$-\frac{5}{8}$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{1}{4} & -\frac{1}{4} & \frac{1}{2} \\
+ -\frac{3}{2} & \frac{1}{4} & \frac{9}{4} \\
+ \frac{3}{2} & -\frac{7}{4} & \frac{9}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{5}{2} & 1 & \frac{7}{4} \\
+ \frac{1}{4} & \frac{1}{2} & -2 \\
+ -\frac{7}{4} & -1 & 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{25}{16} & -\frac{7}{8} & \frac{25}{16} \\
+ -\frac{61}{8} & -\frac{29}{8} & \frac{29}{8} \\
+ -\frac{5}{8} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{3}{2}+\left(-\frac{7}{4}\right)\, \times \, \frac{1}{2}+\frac{9 (-1)}{4}=-\frac{13}{8}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{1}{4} & -\frac{1}{4} & \frac{1}{2} \\
+ -\frac{3}{2} & \frac{1}{4} & \frac{9}{4} \\
+ \frac{3}{2} & -\frac{7}{4} & \frac{9}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{5}{2} & 1 & \frac{7}{4} \\
+ \frac{1}{4} & \frac{1}{2} & -2 \\
+ -\frac{7}{4} & -1 & 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{25}{16} & -\frac{7}{8} & \frac{25}{16} \\
+ -\frac{61}{8} & -\frac{29}{8} & \frac{29}{8} \\
+ -\frac{5}{8} & \fbox{$-\frac{13}{8}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{1}{4} & -\frac{1}{4} & \frac{1}{2} \\
+ -\frac{3}{2} & \frac{1}{4} & \frac{9}{4} \\
+ \frac{3}{2} & -\frac{7}{4} & \frac{9}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{5}{2} & 1 & \frac{7}{4} \\
+ \frac{1}{4} & \frac{1}{2} & -2 \\
+ -\frac{7}{4} & -1 & 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{25}{16} & -\frac{7}{8} & \frac{25}{16} \\
+ -\frac{61}{8} & -\frac{29}{8} & \frac{29}{8} \\
+ -\frac{5}{8} & -\frac{13}{8} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{3\ 7}{2\ 4}+\left(-\frac{7}{4}\right)\, (-2)+\frac{9\ 3}{4}=\frac{103}{8}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ -\frac{1}{4} & -\frac{1}{4} & \frac{1}{2} \\
+ -\frac{3}{2} & \frac{1}{4} & \frac{9}{4} \\
+ \frac{3}{2} & -\frac{7}{4} & \frac{9}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{5}{2} & 1 & \frac{7}{4} \\
+ \frac{1}{4} & \frac{1}{2} & -2 \\
+ -\frac{7}{4} & -1 & 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{25}{16} & -\frac{7}{8} & \frac{25}{16} \\
+ -\frac{61}{8} & -\frac{29}{8} & \frac{29}{8} \\
+ -\frac{5}{8} & -\frac{13}{8} & \fbox{$\frac{103}{8}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/1059.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/1059.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d98a7d95bd82b12e20574e1b86a3d7415f36654e
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/1059.txt
@@ -0,0 +1,166 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ \frac{7}{8} & -\frac{15}{8} & -\frac{5}{2} \\
+ 2 & -1 & -\frac{13}{8} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ \frac{17}{8} \\
+ -\frac{11}{8} \\
+ -\frac{7}{8} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{7}{8} & -\frac{15}{8} & -\frac{5}{2} \\
+ 2 & -1 & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{17}{8} \\
+ -\frac{11}{8} \\
+ -\frac{7}{8} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{7}{8} & -\frac{15}{8} & -\frac{5}{2} \\
+ 2 & -1 & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{17}{8} \\
+ -\frac{11}{8} \\
+ -\frac{7}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{7}{8} & -\frac{15}{8} & -\frac{5}{2} \\
+ 2 & -1 & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{17}{8} \\
+ -\frac{11}{8} \\
+ -\frac{7}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{7\ 17}{8\ 8}+\left(-\frac{15}{8}\right)\, \left(-\frac{11}{8}\right)+\left(-\frac{5}{2}\right)\, \left(-\frac{7}{8}\right)=\frac{53}{8}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{7}{8} & -\frac{15}{8} & -\frac{5}{2} \\
+ 2 & -1 & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{17}{8} \\
+ -\frac{11}{8} \\
+ -\frac{7}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$\frac{53}{8}$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{7}{8} & -\frac{15}{8} & -\frac{5}{2} \\
+ 2 & -1 & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{17}{8} \\
+ -\frac{11}{8} \\
+ -\frac{7}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \frac{53}{8} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2\ 17}{8}+(-1)\, \left(-\frac{11}{8}\right)+\left(-\frac{13}{8}\right)\, \left(-\frac{7}{8}\right)=\frac{451}{64}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ \frac{7}{8} & -\frac{15}{8} & -\frac{5}{2} \\
+ 2 & -1 & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{17}{8} \\
+ -\frac{11}{8} \\
+ -\frac{7}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \frac{53}{8} \\
+ \fbox{$\frac{451}{64}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/1179.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/1179.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e4dae13f11bc5adbaa6ec7185e02eef45557eb7e
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/1179.txt
@@ -0,0 +1,549 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ \frac{4}{5} & \frac{9}{5} & \frac{13}{5} \\
+ \frac{7}{5} & 1 & -\frac{2}{5} \\
+ \frac{13}{5} & -3 & -\frac{13}{5} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ -\frac{13}{5} & 3 & -\frac{11}{5} \\
+ -\frac{13}{5} & -\frac{8}{5} & 1 \\
+ -\frac{2}{5} & -2 & -\frac{13}{5} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{4}{5} & \frac{9}{5} & \frac{13}{5} \\
+ \frac{7}{5} & 1 & -\frac{2}{5} \\
+ \frac{13}{5} & -3 & -\frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{13}{5} & 3 & -\frac{11}{5} \\
+ -\frac{13}{5} & -\frac{8}{5} & 1 \\
+ -\frac{2}{5} & -2 & -\frac{13}{5} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{4}{5} & \frac{9}{5} & \frac{13}{5} \\
+ \frac{7}{5} & 1 & -\frac{2}{5} \\
+ \frac{13}{5} & -3 & -\frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{13}{5} & 3 & -\frac{11}{5} \\
+ -\frac{13}{5} & -\frac{8}{5} & 1 \\
+ -\frac{2}{5} & -2 & -\frac{13}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{4}{5} & \frac{9}{5} & \frac{13}{5} \\
+ \frac{7}{5} & 1 & -\frac{2}{5} \\
+ \frac{13}{5} & -3 & -\frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{13}{5} & 3 & -\frac{11}{5} \\
+ -\frac{13}{5} & -\frac{8}{5} & 1 \\
+ -\frac{2}{5} & -2 & -\frac{13}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{4 (-13)}{5\ 5}+\frac{9 (-13)}{5\ 5}+\frac{13 (-2)}{5\ 5}=-\frac{39}{5}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{4}{5} & \frac{9}{5} & \frac{13}{5} \\
+ \frac{7}{5} & 1 & -\frac{2}{5} \\
+ \frac{13}{5} & -3 & -\frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{13}{5} & 3 & -\frac{11}{5} \\
+ -\frac{13}{5} & -\frac{8}{5} & 1 \\
+ -\frac{2}{5} & -2 & -\frac{13}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$-\frac{39}{5}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{4}{5} & \frac{9}{5} & \frac{13}{5} \\
+ \frac{7}{5} & 1 & -\frac{2}{5} \\
+ \frac{13}{5} & -3 & -\frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{13}{5} & 3 & -\frac{11}{5} \\
+ -\frac{13}{5} & -\frac{8}{5} & 1 \\
+ -\frac{2}{5} & -2 & -\frac{13}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{39}{5} & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{4\ 3}{5}+\frac{9 (-8)}{5\ 5}+\frac{13 (-2)}{5}=-\frac{142}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{4}{5} & \frac{9}{5} & \frac{13}{5} \\
+ \frac{7}{5} & 1 & -\frac{2}{5} \\
+ \frac{13}{5} & -3 & -\frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{13}{5} & 3 & -\frac{11}{5} \\
+ -\frac{13}{5} & -\frac{8}{5} & 1 \\
+ -\frac{2}{5} & -2 & -\frac{13}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{39}{5} & \fbox{$-\frac{142}{25}$} & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{4}{5} & \frac{9}{5} & \frac{13}{5} \\
+ \frac{7}{5} & 1 & -\frac{2}{5} \\
+ \frac{13}{5} & -3 & -\frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{13}{5} & 3 & -\frac{11}{5} \\
+ -\frac{13}{5} & -\frac{8}{5} & 1 \\
+ -\frac{2}{5} & -2 & -\frac{13}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{39}{5} & -\frac{142}{25} & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{4 (-11)}{5\ 5}+\frac{9}{5}+\frac{13 (-13)}{5\ 5}=-\frac{168}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{4}{5} & \frac{9}{5} & \frac{13}{5} \\
+ \frac{7}{5} & 1 & -\frac{2}{5} \\
+ \frac{13}{5} & -3 & -\frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{13}{5} & 3 & -\frac{11}{5} \\
+ -\frac{13}{5} & -\frac{8}{5} & 1 \\
+ -\frac{2}{5} & -2 & -\frac{13}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{39}{5} & -\frac{142}{25} & \fbox{$-\frac{168}{25}$} \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{4}{5} & \frac{9}{5} & \frac{13}{5} \\
+ \frac{7}{5} & 1 & -\frac{2}{5} \\
+ \frac{13}{5} & -3 & -\frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{13}{5} & 3 & -\frac{11}{5} \\
+ -\frac{13}{5} & -\frac{8}{5} & 1 \\
+ -\frac{2}{5} & -2 & -\frac{13}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{39}{5} & -\frac{142}{25} & -\frac{168}{25} \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{7 (-13)}{5\ 5}-\frac{13}{5}+\left(-\frac{2}{5}\right)\, \left(-\frac{2}{5}\right)=-\frac{152}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{4}{5} & \frac{9}{5} & \frac{13}{5} \\
+ \frac{7}{5} & 1 & -\frac{2}{5} \\
+ \frac{13}{5} & -3 & -\frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{13}{5} & 3 & -\frac{11}{5} \\
+ -\frac{13}{5} & -\frac{8}{5} & 1 \\
+ -\frac{2}{5} & -2 & -\frac{13}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{39}{5} & -\frac{142}{25} & -\frac{168}{25} \\
+ \fbox{$-\frac{152}{25}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{4}{5} & \frac{9}{5} & \frac{13}{5} \\
+ \frac{7}{5} & 1 & -\frac{2}{5} \\
+ \frac{13}{5} & -3 & -\frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{13}{5} & 3 & -\frac{11}{5} \\
+ -\frac{13}{5} & -\frac{8}{5} & 1 \\
+ -\frac{2}{5} & -2 & -\frac{13}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{39}{5} & -\frac{142}{25} & -\frac{168}{25} \\
+ -\frac{152}{25} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{7\ 3}{5}-\frac{8}{5}+\left(-\frac{2}{5}\right)\, (-2)=\frac{17}{5}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{4}{5} & \frac{9}{5} & \frac{13}{5} \\
+ \frac{7}{5} & 1 & -\frac{2}{5} \\
+ \frac{13}{5} & -3 & -\frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{13}{5} & 3 & -\frac{11}{5} \\
+ -\frac{13}{5} & -\frac{8}{5} & 1 \\
+ -\frac{2}{5} & -2 & -\frac{13}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{39}{5} & -\frac{142}{25} & -\frac{168}{25} \\
+ -\frac{152}{25} & \fbox{$\frac{17}{5}$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{4}{5} & \frac{9}{5} & \frac{13}{5} \\
+ \frac{7}{5} & 1 & -\frac{2}{5} \\
+ \frac{13}{5} & -3 & -\frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{13}{5} & 3 & -\frac{11}{5} \\
+ -\frac{13}{5} & -\frac{8}{5} & 1 \\
+ -\frac{2}{5} & -2 & -\frac{13}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{39}{5} & -\frac{142}{25} & -\frac{168}{25} \\
+ -\frac{152}{25} & \frac{17}{5} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{7 (-11)}{5\ 5}+1\ 1+\left(-\frac{2}{5}\right)\, \left(-\frac{13}{5}\right)=-\frac{26}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{4}{5} & \frac{9}{5} & \frac{13}{5} \\
+ \frac{7}{5} & 1 & -\frac{2}{5} \\
+ \frac{13}{5} & -3 & -\frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{13}{5} & 3 & -\frac{11}{5} \\
+ -\frac{13}{5} & -\frac{8}{5} & 1 \\
+ -\frac{2}{5} & -2 & -\frac{13}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{39}{5} & -\frac{142}{25} & -\frac{168}{25} \\
+ -\frac{152}{25} & \frac{17}{5} & \fbox{$-\frac{26}{25}$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{4}{5} & \frac{9}{5} & \frac{13}{5} \\
+ \frac{7}{5} & 1 & -\frac{2}{5} \\
+ \frac{13}{5} & -3 & -\frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{13}{5} & 3 & -\frac{11}{5} \\
+ -\frac{13}{5} & -\frac{8}{5} & 1 \\
+ -\frac{2}{5} & -2 & -\frac{13}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{39}{5} & -\frac{142}{25} & -\frac{168}{25} \\
+ -\frac{152}{25} & \frac{17}{5} & -\frac{26}{25} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{13 (-13)}{5\ 5}+(-3)\, \left(-\frac{13}{5}\right)+\left(-\frac{13}{5}\right)\, \left(-\frac{2}{5}\right)=\frac{52}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{4}{5} & \frac{9}{5} & \frac{13}{5} \\
+ \frac{7}{5} & 1 & -\frac{2}{5} \\
+ \frac{13}{5} & -3 & -\frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{13}{5} & 3 & -\frac{11}{5} \\
+ -\frac{13}{5} & -\frac{8}{5} & 1 \\
+ -\frac{2}{5} & -2 & -\frac{13}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{39}{5} & -\frac{142}{25} & -\frac{168}{25} \\
+ -\frac{152}{25} & \frac{17}{5} & -\frac{26}{25} \\
+ \fbox{$\frac{52}{25}$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{4}{5} & \frac{9}{5} & \frac{13}{5} \\
+ \frac{7}{5} & 1 & -\frac{2}{5} \\
+ \frac{13}{5} & -3 & -\frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{13}{5} & 3 & -\frac{11}{5} \\
+ -\frac{13}{5} & -\frac{8}{5} & 1 \\
+ -\frac{2}{5} & -2 & -\frac{13}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{39}{5} & -\frac{142}{25} & -\frac{168}{25} \\
+ -\frac{152}{25} & \frac{17}{5} & -\frac{26}{25} \\
+ \frac{52}{25} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{13\ 3}{5}+(-3)\, \left(-\frac{8}{5}\right)+\left(-\frac{13}{5}\right)\, (-2)=\frac{89}{5}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{4}{5} & \frac{9}{5} & \frac{13}{5} \\
+ \frac{7}{5} & 1 & -\frac{2}{5} \\
+ \frac{13}{5} & -3 & -\frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{13}{5} & 3 & -\frac{11}{5} \\
+ -\frac{13}{5} & -\frac{8}{5} & 1 \\
+ -\frac{2}{5} & -2 & -\frac{13}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{39}{5} & -\frac{142}{25} & -\frac{168}{25} \\
+ -\frac{152}{25} & \frac{17}{5} & -\frac{26}{25} \\
+ \frac{52}{25} & \fbox{$\frac{89}{5}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{4}{5} & \frac{9}{5} & \frac{13}{5} \\
+ \frac{7}{5} & 1 & -\frac{2}{5} \\
+ \frac{13}{5} & -3 & -\frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{13}{5} & 3 & -\frac{11}{5} \\
+ -\frac{13}{5} & -\frac{8}{5} & 1 \\
+ -\frac{2}{5} & -2 & -\frac{13}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{39}{5} & -\frac{142}{25} & -\frac{168}{25} \\
+ -\frac{152}{25} & \frac{17}{5} & -\frac{26}{25} \\
+ \frac{52}{25} & \frac{89}{5} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{13 (-11)}{5\ 5}+(-3)\, \times \, 1+\left(-\frac{13}{5}\right)\, \left(-\frac{13}{5}\right)=-\frac{49}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ \frac{4}{5} & \frac{9}{5} & \frac{13}{5} \\
+ \frac{7}{5} & 1 & -\frac{2}{5} \\
+ \frac{13}{5} & -3 & -\frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{13}{5} & 3 & -\frac{11}{5} \\
+ -\frac{13}{5} & -\frac{8}{5} & 1 \\
+ -\frac{2}{5} & -2 & -\frac{13}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{39}{5} & -\frac{142}{25} & -\frac{168}{25} \\
+ -\frac{152}{25} & \frac{17}{5} & -\frac{26}{25} \\
+ \frac{52}{25} & \frac{89}{5} & \fbox{$-\frac{49}{25}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/1180.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/1180.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d979fa704f5bc285b25ee3763d559c997878b7de
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/1180.txt
@@ -0,0 +1,166 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ -3 & 0 & 0 \\
+ -1 & 1 & -1 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -1 \\
+ 0 \\
+ -2 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ -3 & 0 & 0 \\
+ -1 & 1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -1 \\
+ 0 \\
+ -2 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -3 & 0 & 0 \\
+ -1 & 1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -1 \\
+ 0 \\
+ -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -3 & 0 & 0 \\
+ -1 & 1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -1 \\
+ 0 \\
+ -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-3)\, (-1)+0\ 0+0 (-2)=3. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -3 & 0 & 0 \\
+ -1 & 1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -1 \\
+ 0 \\
+ -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$3$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -3 & 0 & 0 \\
+ -1 & 1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -1 \\
+ 0 \\
+ -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 3 \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, (-1)+1\ 0+(-1)\, (-2)=3. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ -3 & 0 & 0 \\
+ -1 & 1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -1 \\
+ 0 \\
+ -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 3 \\
+ \fbox{$3$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/1228.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/1228.txt
new file mode 100644
index 0000000000000000000000000000000000000000..31be9131c235cc4b1d364863ddcdee6c056ffef6
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/1228.txt
@@ -0,0 +1,231 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{2}{5} & -\frac{14}{5} \\
+ -\frac{9}{5} & -\frac{11}{5} & -\frac{9}{5} \\
+ -\frac{7}{5} & \frac{3}{5} & \frac{9}{5} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -\frac{12}{5} \\
+ \frac{7}{5} \\
+ -\frac{6}{5} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{2}{5} & -\frac{14}{5} \\
+ -\frac{9}{5} & -\frac{11}{5} & -\frac{9}{5} \\
+ -\frac{7}{5} & \frac{3}{5} & \frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -\frac{12}{5} \\
+ \frac{7}{5} \\
+ -\frac{6}{5} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{2}{5} & -\frac{14}{5} \\
+ -\frac{9}{5} & -\frac{11}{5} & -\frac{9}{5} \\
+ -\frac{7}{5} & \frac{3}{5} & \frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -\frac{12}{5} \\
+ \frac{7}{5} \\
+ -\frac{6}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{2}{5} & -\frac{14}{5} \\
+ -\frac{9}{5} & -\frac{11}{5} & -\frac{9}{5} \\
+ -\frac{7}{5} & \frac{3}{5} & \frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -\frac{12}{5} \\
+ \frac{7}{5} \\
+ -\frac{6}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{7}{5}\right)\, \left(-\frac{12}{5}\right)+\frac{2\ 7}{5\ 5}+\left(-\frac{14}{5}\right)\, \left(-\frac{6}{5}\right)=\frac{182}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{2}{5} & -\frac{14}{5} \\
+ -\frac{9}{5} & -\frac{11}{5} & -\frac{9}{5} \\
+ -\frac{7}{5} & \frac{3}{5} & \frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -\frac{12}{5} \\
+ \frac{7}{5} \\
+ -\frac{6}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$\frac{182}{25}$} \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{2}{5} & -\frac{14}{5} \\
+ -\frac{9}{5} & -\frac{11}{5} & -\frac{9}{5} \\
+ -\frac{7}{5} & \frac{3}{5} & \frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -\frac{12}{5} \\
+ \frac{7}{5} \\
+ -\frac{6}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \frac{182}{25} \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{9}{5}\right)\, \left(-\frac{12}{5}\right)+\left(-\frac{11}{5}\right)\, \times \, \frac{7}{5}+\left(-\frac{9}{5}\right)\, \left(-\frac{6}{5}\right)=\frac{17}{5}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{2}{5} & -\frac{14}{5} \\
+ -\frac{9}{5} & -\frac{11}{5} & -\frac{9}{5} \\
+ -\frac{7}{5} & \frac{3}{5} & \frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -\frac{12}{5} \\
+ \frac{7}{5} \\
+ -\frac{6}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \frac{182}{25} \\
+ \fbox{$\frac{17}{5}$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{2}{5} & -\frac{14}{5} \\
+ -\frac{9}{5} & -\frac{11}{5} & -\frac{9}{5} \\
+ -\frac{7}{5} & \frac{3}{5} & \frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -\frac{12}{5} \\
+ \frac{7}{5} \\
+ -\frac{6}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \frac{182}{25} \\
+ \frac{17}{5} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{7}{5}\right)\, \left(-\frac{12}{5}\right)+\frac{3\ 7}{5\ 5}+\frac{9 (-6)}{5\ 5}=\frac{51}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{2}{5} & -\frac{14}{5} \\
+ -\frac{9}{5} & -\frac{11}{5} & -\frac{9}{5} \\
+ -\frac{7}{5} & \frac{3}{5} & \frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -\frac{12}{5} \\
+ \frac{7}{5} \\
+ -\frac{6}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \frac{182}{25} \\
+ \frac{17}{5} \\
+ \fbox{$\frac{51}{25}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/124.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/124.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e3822ddc13257aa0e7dc274b221fc212c8b11478
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/124.txt
@@ -0,0 +1,347 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ -1 & -1 \\
+ 2 & -1 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ -2 & -2 & 0 \\
+ 0 & 1 & 1 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ -1 & -1 \\
+ 2 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & -2 & 0 \\
+ 0 & 1 & 1 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -1 & -1 \\
+ 2 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & -2 & 0 \\
+ 0 & 1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -1 & -1 \\
+ 2 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & -2 & 0 \\
+ 0 & 1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, (-2)+(-1)\, \times \, 0=2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -1 & -1 \\
+ 2 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & -2 & 0 \\
+ 0 & 1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$2$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -1 & -1 \\
+ 2 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & -2 & 0 \\
+ 0 & 1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 2 & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, (-2)+(-1)\, \times \, 1=1. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -1 & -1 \\
+ 2 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & -2 & 0 \\
+ 0 & 1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 2 & \fbox{$1$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -1 & -1 \\
+ 2 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & -2 & 0 \\
+ 0 & 1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 2 & 1 & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, \times \, 0+(-1)\, \times \, 1=-1. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -1 & -1 \\
+ 2 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & -2 & 0 \\
+ 0 & 1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 2 & 1 & \fbox{$-1$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -1 & -1 \\
+ 2 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & -2 & 0 \\
+ 0 & 1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 2 & 1 & -1 \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2 (-2)+(-1)\, \times \, 0=-4. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -1 & -1 \\
+ 2 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & -2 & 0 \\
+ 0 & 1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 2 & 1 & -1 \\
+ \fbox{$-4$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -1 & -1 \\
+ 2 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & -2 & 0 \\
+ 0 & 1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 2 & 1 & -1 \\
+ -4 & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2 (-2)+(-1)\, \times \, 1=-5. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -1 & -1 \\
+ 2 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & -2 & 0 \\
+ 0 & 1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 2 & 1 & -1 \\
+ -4 & \fbox{$-5$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -1 & -1 \\
+ 2 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & -2 & 0 \\
+ 0 & 1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 2 & 1 & -1 \\
+ -4 & -5 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2\ 0+(-1)\, \times \, 1=-1. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ -1 & -1 \\
+ 2 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & -2 & 0 \\
+ 0 & 1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 2 & 1 & -1 \\
+ -4 & -5 & \fbox{$-1$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/1241.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/1241.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f00ec0f30ee7e4305b14d8a5b9b98b7654c2c2fd
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/1241.txt
@@ -0,0 +1,347 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ -\frac{12}{5} & \frac{13}{5} \\
+ -\frac{6}{5} & -\frac{4}{5} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ \frac{12}{5} & -3 & -2 \\
+ -3 & 3 & -\frac{11}{5} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{12}{5} & \frac{13}{5} \\
+ -\frac{6}{5} & -\frac{4}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{12}{5} & -3 & -2 \\
+ -3 & 3 & -\frac{11}{5} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{12}{5} & \frac{13}{5} \\
+ -\frac{6}{5} & -\frac{4}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{12}{5} & -3 & -2 \\
+ -3 & 3 & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{12}{5} & \frac{13}{5} \\
+ -\frac{6}{5} & -\frac{4}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{12}{5} & -3 & -2 \\
+ -3 & 3 & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{12}{5}\right)\, \times \, \frac{12}{5}+\frac{13 (-3)}{5}=-\frac{339}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{12}{5} & \frac{13}{5} \\
+ -\frac{6}{5} & -\frac{4}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{12}{5} & -3 & -2 \\
+ -3 & 3 & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$-\frac{339}{25}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{12}{5} & \frac{13}{5} \\
+ -\frac{6}{5} & -\frac{4}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{12}{5} & -3 & -2 \\
+ -3 & 3 & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{339}{25} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{12}{5}\right)\, (-3)+\frac{13\ 3}{5}=15. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{12}{5} & \frac{13}{5} \\
+ -\frac{6}{5} & -\frac{4}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{12}{5} & -3 & -2 \\
+ -3 & 3 & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{339}{25} & \fbox{$15$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{12}{5} & \frac{13}{5} \\
+ -\frac{6}{5} & -\frac{4}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{12}{5} & -3 & -2 \\
+ -3 & 3 & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{339}{25} & 15 & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{12}{5}\right)\, (-2)+\frac{13 (-11)}{5\ 5}=-\frac{23}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{12}{5} & \frac{13}{5} \\
+ -\frac{6}{5} & -\frac{4}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{12}{5} & -3 & -2 \\
+ -3 & 3 & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{339}{25} & 15 & \fbox{$-\frac{23}{25}$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{12}{5} & \frac{13}{5} \\
+ -\frac{6}{5} & -\frac{4}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{12}{5} & -3 & -2 \\
+ -3 & 3 & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{339}{25} & 15 & -\frac{23}{25} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{6}{5}\right)\, \times \, \frac{12}{5}+\left(-\frac{4}{5}\right)\, (-3)=-\frac{12}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{12}{5} & \frac{13}{5} \\
+ -\frac{6}{5} & -\frac{4}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{12}{5} & -3 & -2 \\
+ -3 & 3 & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{339}{25} & 15 & -\frac{23}{25} \\
+ \fbox{$-\frac{12}{25}$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{12}{5} & \frac{13}{5} \\
+ -\frac{6}{5} & -\frac{4}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{12}{5} & -3 & -2 \\
+ -3 & 3 & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{339}{25} & 15 & -\frac{23}{25} \\
+ -\frac{12}{25} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{6}{5}\right)\, (-3)+\left(-\frac{4}{5}\right)\, \times \, 3=\frac{6}{5}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{12}{5} & \frac{13}{5} \\
+ -\frac{6}{5} & -\frac{4}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{12}{5} & -3 & -2 \\
+ -3 & 3 & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{339}{25} & 15 & -\frac{23}{25} \\
+ -\frac{12}{25} & \fbox{$\frac{6}{5}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{12}{5} & \frac{13}{5} \\
+ -\frac{6}{5} & -\frac{4}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{12}{5} & -3 & -2 \\
+ -3 & 3 & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{339}{25} & 15 & -\frac{23}{25} \\
+ -\frac{12}{25} & \frac{6}{5} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{6}{5}\right)\, (-2)+\left(-\frac{4}{5}\right)\, \left(-\frac{11}{5}\right)=\frac{104}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ -\frac{12}{5} & \frac{13}{5} \\
+ -\frac{6}{5} & -\frac{4}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{12}{5} & -3 & -2 \\
+ -3 & 3 & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{339}{25} & 15 & -\frac{23}{25} \\
+ -\frac{12}{25} & \frac{6}{5} & \fbox{$\frac{104}{25}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/125.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/125.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1c69e1fbf660fa0d31277cc7407c5e7ce98a9f82
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/125.txt
@@ -0,0 +1,390 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ -\frac{13}{5} & -\frac{8}{5} & \frac{7}{5} \\
+ -\frac{2}{5} & \frac{6}{5} & -\frac{1}{5} \\
+ -\frac{6}{5} & \frac{14}{5} & -\frac{11}{5} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{cc}
+ \frac{14}{5} & -\frac{7}{5} \\
+ 1 & 1 \\
+ -\frac{4}{5} & -\frac{11}{5} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{13}{5} & -\frac{8}{5} & \frac{7}{5} \\
+ -\frac{2}{5} & \frac{6}{5} & -\frac{1}{5} \\
+ -\frac{6}{5} & \frac{14}{5} & -\frac{11}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{14}{5} & -\frac{7}{5} \\
+ 1 & 1 \\
+ -\frac{4}{5} & -\frac{11}{5} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 2. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 2: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{13}{5} & -\frac{8}{5} & \frac{7}{5} \\
+ -\frac{2}{5} & \frac{6}{5} & -\frac{1}{5} \\
+ -\frac{6}{5} & \frac{14}{5} & -\frac{11}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{14}{5} & -\frac{7}{5} \\
+ 1 & 1 \\
+ -\frac{4}{5} & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{13}{5} & -\frac{8}{5} & \frac{7}{5} \\
+ -\frac{2}{5} & \frac{6}{5} & -\frac{1}{5} \\
+ -\frac{6}{5} & \frac{14}{5} & -\frac{11}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{14}{5} & -\frac{7}{5} \\
+ 1 & 1 \\
+ -\frac{4}{5} & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{13}{5}\right)\, \times \, \frac{14}{5}+\left(-\frac{8}{5}\right)\, \times \, 1+\frac{7 (-4)}{5\ 5}=-10. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{13}{5} & -\frac{8}{5} & \frac{7}{5} \\
+ -\frac{2}{5} & \frac{6}{5} & -\frac{1}{5} \\
+ -\frac{6}{5} & \frac{14}{5} & -\frac{11}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{14}{5} & -\frac{7}{5} \\
+ 1 & 1 \\
+ -\frac{4}{5} & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \fbox{$-10$} & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{13}{5} & -\frac{8}{5} & \frac{7}{5} \\
+ -\frac{2}{5} & \frac{6}{5} & -\frac{1}{5} \\
+ -\frac{6}{5} & \frac{14}{5} & -\frac{11}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{14}{5} & -\frac{7}{5} \\
+ 1 & 1 \\
+ -\frac{4}{5} & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -10 & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{13}{5}\right)\, \left(-\frac{7}{5}\right)+\left(-\frac{8}{5}\right)\, \times \, 1+\frac{7 (-11)}{5\ 5}=-\frac{26}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{13}{5} & -\frac{8}{5} & \frac{7}{5} \\
+ -\frac{2}{5} & \frac{6}{5} & -\frac{1}{5} \\
+ -\frac{6}{5} & \frac{14}{5} & -\frac{11}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{14}{5} & -\frac{7}{5} \\
+ 1 & 1 \\
+ -\frac{4}{5} & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -10 & \fbox{$-\frac{26}{25}$} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{13}{5} & -\frac{8}{5} & \frac{7}{5} \\
+ -\frac{2}{5} & \frac{6}{5} & -\frac{1}{5} \\
+ -\frac{6}{5} & \frac{14}{5} & -\frac{11}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{14}{5} & -\frac{7}{5} \\
+ 1 & 1 \\
+ -\frac{4}{5} & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -10 & -\frac{26}{25} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{2}{5}\right)\, \times \, \frac{14}{5}+\frac{6}{5}+\frac{4}{5\ 5}=\frac{6}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{13}{5} & -\frac{8}{5} & \frac{7}{5} \\
+ -\frac{2}{5} & \frac{6}{5} & -\frac{1}{5} \\
+ -\frac{6}{5} & \frac{14}{5} & -\frac{11}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{14}{5} & -\frac{7}{5} \\
+ 1 & 1 \\
+ -\frac{4}{5} & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -10 & -\frac{26}{25} \\
+ \fbox{$\frac{6}{25}$} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{13}{5} & -\frac{8}{5} & \frac{7}{5} \\
+ -\frac{2}{5} & \frac{6}{5} & -\frac{1}{5} \\
+ -\frac{6}{5} & \frac{14}{5} & -\frac{11}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{14}{5} & -\frac{7}{5} \\
+ 1 & 1 \\
+ -\frac{4}{5} & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -10 & -\frac{26}{25} \\
+ \frac{6}{25} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{2}{5}\right)\, \left(-\frac{7}{5}\right)+\frac{6}{5}+\frac{11}{5\ 5}=\frac{11}{5}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{13}{5} & -\frac{8}{5} & \frac{7}{5} \\
+ -\frac{2}{5} & \frac{6}{5} & -\frac{1}{5} \\
+ -\frac{6}{5} & \frac{14}{5} & -\frac{11}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{14}{5} & -\frac{7}{5} \\
+ 1 & 1 \\
+ -\frac{4}{5} & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -10 & -\frac{26}{25} \\
+ \frac{6}{25} & \fbox{$\frac{11}{5}$} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{13}{5} & -\frac{8}{5} & \frac{7}{5} \\
+ -\frac{2}{5} & \frac{6}{5} & -\frac{1}{5} \\
+ -\frac{6}{5} & \frac{14}{5} & -\frac{11}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{14}{5} & -\frac{7}{5} \\
+ 1 & 1 \\
+ -\frac{4}{5} & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -10 & -\frac{26}{25} \\
+ \frac{6}{25} & \frac{11}{5} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{6}{5}\right)\, \times \, \frac{14}{5}+\frac{14}{5}+\left(-\frac{11}{5}\right)\, \left(-\frac{4}{5}\right)=\frac{6}{5}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{13}{5} & -\frac{8}{5} & \frac{7}{5} \\
+ -\frac{2}{5} & \frac{6}{5} & -\frac{1}{5} \\
+ -\frac{6}{5} & \frac{14}{5} & -\frac{11}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{14}{5} & -\frac{7}{5} \\
+ 1 & 1 \\
+ -\frac{4}{5} & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -10 & -\frac{26}{25} \\
+ \frac{6}{25} & \frac{11}{5} \\
+ \fbox{$\frac{6}{5}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{13}{5} & -\frac{8}{5} & \frac{7}{5} \\
+ -\frac{2}{5} & \frac{6}{5} & -\frac{1}{5} \\
+ -\frac{6}{5} & \frac{14}{5} & -\frac{11}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{14}{5} & -\frac{7}{5} \\
+ 1 & 1 \\
+ -\frac{4}{5} & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -10 & -\frac{26}{25} \\
+ \frac{6}{25} & \frac{11}{5} \\
+ \frac{6}{5} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{6}{5}\right)\, \left(-\frac{7}{5}\right)+\frac{14}{5}+\left(-\frac{11}{5}\right)\, \left(-\frac{11}{5}\right)=\frac{233}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ -\frac{13}{5} & -\frac{8}{5} & \frac{7}{5} \\
+ -\frac{2}{5} & \frac{6}{5} & -\frac{1}{5} \\
+ -\frac{6}{5} & \frac{14}{5} & -\frac{11}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{14}{5} & -\frac{7}{5} \\
+ 1 & 1 \\
+ -\frac{4}{5} & -\frac{11}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -10 & -\frac{26}{25} \\
+ \frac{6}{25} & \frac{11}{5} \\
+ \frac{6}{5} & \fbox{$\frac{233}{25}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/127.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/127.txt
new file mode 100644
index 0000000000000000000000000000000000000000..44042bf1ab3e36f5becf678d6a0226281d9bac40
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/127.txt
@@ -0,0 +1,231 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ 0 & -1 & -2 \\
+ -2 & 1 & 2 \\
+ -1 & -3 & 3 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -3 \\
+ 1 \\
+ -1 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ 0 & -1 & -2 \\
+ -2 & 1 & 2 \\
+ -1 & -3 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -3 \\
+ 1 \\
+ -1 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 0 & -1 & -2 \\
+ -2 & 1 & 2 \\
+ -1 & -3 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -3 \\
+ 1 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 0 & -1 & -2 \\
+ -2 & 1 & 2 \\
+ -1 & -3 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -3 \\
+ 1 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0 (-3)+(-1)\, \times \, 1+(-2)\, (-1)=1. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 0 & -1 & -2 \\
+ -2 & 1 & 2 \\
+ -1 & -3 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -3 \\
+ 1 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$1$} \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 0 & -1 & -2 \\
+ -2 & 1 & 2 \\
+ -1 & -3 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -3 \\
+ 1 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 1 \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, (-3)+1\ 1+2 (-1)=5. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 0 & -1 & -2 \\
+ -2 & 1 & 2 \\
+ -1 & -3 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -3 \\
+ 1 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 1 \\
+ \fbox{$5$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 0 & -1 & -2 \\
+ -2 & 1 & 2 \\
+ -1 & -3 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -3 \\
+ 1 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 1 \\
+ 5 \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, (-3)+(-3)\, \times \, 1+3 (-1)=-3. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ 0 & -1 & -2 \\
+ -2 & 1 & 2 \\
+ -1 & -3 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -3 \\
+ 1 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 1 \\
+ 5 \\
+ \fbox{$-3$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/132.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/132.txt
new file mode 100644
index 0000000000000000000000000000000000000000..873b68aaf6ec82df3a48893baaccf497d46563ee
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/132.txt
@@ -0,0 +1,347 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ -2 & \frac{9}{4} \\
+ \frac{3}{4} & \frac{5}{4} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ -\frac{1}{2} & \frac{1}{2} & 0 \\
+ -\frac{3}{4} & 2 & -\frac{3}{2} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ -2 & \frac{9}{4} \\
+ \frac{3}{4} & \frac{5}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{2} & \frac{1}{2} & 0 \\
+ -\frac{3}{4} & 2 & -\frac{3}{2} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -2 & \frac{9}{4} \\
+ \frac{3}{4} & \frac{5}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{2} & \frac{1}{2} & 0 \\
+ -\frac{3}{4} & 2 & -\frac{3}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -2 & \frac{9}{4} \\
+ \frac{3}{4} & \frac{5}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{2} & \frac{1}{2} & 0 \\
+ -\frac{3}{4} & 2 & -\frac{3}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2}{2}+\frac{9 (-3)}{4\ 4}=-\frac{11}{16}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -2 & \frac{9}{4} \\
+ \frac{3}{4} & \frac{5}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{2} & \frac{1}{2} & 0 \\
+ -\frac{3}{4} & 2 & -\frac{3}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$-\frac{11}{16}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -2 & \frac{9}{4} \\
+ \frac{3}{4} & \frac{5}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{2} & \frac{1}{2} & 0 \\
+ -\frac{3}{4} & 2 & -\frac{3}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{11}{16} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, \times \, \frac{1}{2}+\frac{9\ 2}{4}=\frac{7}{2}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -2 & \frac{9}{4} \\
+ \frac{3}{4} & \frac{5}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{2} & \frac{1}{2} & 0 \\
+ -\frac{3}{4} & 2 & -\frac{3}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{11}{16} & \fbox{$\frac{7}{2}$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -2 & \frac{9}{4} \\
+ \frac{3}{4} & \frac{5}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{2} & \frac{1}{2} & 0 \\
+ -\frac{3}{4} & 2 & -\frac{3}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{11}{16} & \frac{7}{2} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, \times \, 0+\frac{9 (-3)}{4\ 2}=-\frac{27}{8}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -2 & \frac{9}{4} \\
+ \frac{3}{4} & \frac{5}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{2} & \frac{1}{2} & 0 \\
+ -\frac{3}{4} & 2 & -\frac{3}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{11}{16} & \frac{7}{2} & \fbox{$-\frac{27}{8}$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -2 & \frac{9}{4} \\
+ \frac{3}{4} & \frac{5}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{2} & \frac{1}{2} & 0 \\
+ -\frac{3}{4} & 2 & -\frac{3}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{11}{16} & \frac{7}{2} & -\frac{27}{8} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{2} \left(-\frac{3}{4}\right)+\frac{5 (-3)}{4\ 4}=-\frac{21}{16}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -2 & \frac{9}{4} \\
+ \frac{3}{4} & \frac{5}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{2} & \frac{1}{2} & 0 \\
+ -\frac{3}{4} & 2 & -\frac{3}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{11}{16} & \frac{7}{2} & -\frac{27}{8} \\
+ \fbox{$-\frac{21}{16}$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -2 & \frac{9}{4} \\
+ \frac{3}{4} & \frac{5}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{2} & \frac{1}{2} & 0 \\
+ -\frac{3}{4} & 2 & -\frac{3}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{11}{16} & \frac{7}{2} & -\frac{27}{8} \\
+ -\frac{21}{16} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{3}{4\ 2}+\frac{5\ 2}{4}=\frac{23}{8}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -2 & \frac{9}{4} \\
+ \frac{3}{4} & \frac{5}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{2} & \frac{1}{2} & 0 \\
+ -\frac{3}{4} & 2 & -\frac{3}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{11}{16} & \frac{7}{2} & -\frac{27}{8} \\
+ -\frac{21}{16} & \fbox{$\frac{23}{8}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -2 & \frac{9}{4} \\
+ \frac{3}{4} & \frac{5}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{2} & \frac{1}{2} & 0 \\
+ -\frac{3}{4} & 2 & -\frac{3}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{11}{16} & \frac{7}{2} & -\frac{27}{8} \\
+ -\frac{21}{16} & \frac{23}{8} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{3\ 0}{4}+\frac{5 (-3)}{4\ 2}=-\frac{15}{8}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ -2 & \frac{9}{4} \\
+ \frac{3}{4} & \frac{5}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{2} & \frac{1}{2} & 0 \\
+ -\frac{3}{4} & 2 & -\frac{3}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{11}{16} & \frac{7}{2} & -\frac{27}{8} \\
+ -\frac{21}{16} & \frac{23}{8} & \fbox{$-\frac{15}{8}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/1364.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/1364.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8e44285a7dcae4ab966b0ea2c12d2c7349be7d2c
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/1364.txt
@@ -0,0 +1,264 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ 3 & 2 & 3 \\
+ -3 & -2 & -2 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{cc}
+ 1 & -2 \\
+ 3 & -3 \\
+ 3 & 1 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ 3 & 2 & 3 \\
+ -3 & -2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -2 \\
+ 3 & -3 \\
+ 3 & 1 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 2. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 2: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 3 & 2 & 3 \\
+ -3 & -2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -2 \\
+ 3 & -3 \\
+ 3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 3 & 2 & 3 \\
+ -3 & -2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -2 \\
+ 3 & -3 \\
+ 3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }3\ 1+2\ 3+3\ 3=18. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 3 & 2 & 3 \\
+ -3 & -2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -2 \\
+ 3 & -3 \\
+ 3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \fbox{$18$} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 3 & 2 & 3 \\
+ -3 & -2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -2 \\
+ 3 & -3 \\
+ 3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 18 & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }3 (-2)+2 (-3)+3\ 1=-9. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 3 & 2 & 3 \\
+ -3 & -2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -2 \\
+ 3 & -3 \\
+ 3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 18 & \fbox{$-9$} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 3 & 2 & 3 \\
+ -3 & -2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -2 \\
+ 3 & -3 \\
+ 3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 18 & -9 \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-3)\, \times \, 1+(-2)\, \times \, 3+(-2)\, \times \, 3=-15. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 3 & 2 & 3 \\
+ -3 & -2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -2 \\
+ 3 & -3 \\
+ 3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 18 & -9 \\
+ \fbox{$-15$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 3 & 2 & 3 \\
+ -3 & -2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -2 \\
+ 3 & -3 \\
+ 3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 18 & -9 \\
+ -15 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-3)\, (-2)+(-2)\, (-3)+(-2)\, \times \, 1=10. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ 3 & 2 & 3 \\
+ -3 & -2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -2 \\
+ 3 & -3 \\
+ 3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 18 & -9 \\
+ -15 & \fbox{$10$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/1405.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/1405.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d895fb18b8cc8ed997d7cd4b7913b3bf18805299
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/1405.txt
@@ -0,0 +1,231 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ \frac{5}{4} & \frac{1}{8} & -\frac{1}{8} \\
+ -\frac{13}{8} & -\frac{1}{16} & -\frac{21}{16} \\
+ -\frac{31}{16} & -\frac{13}{16} & -\frac{33}{16} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ \frac{1}{8} \\
+ \frac{11}{8} \\
+ \frac{43}{16} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{4} & \frac{1}{8} & -\frac{1}{8} \\
+ -\frac{13}{8} & -\frac{1}{16} & -\frac{21}{16} \\
+ -\frac{31}{16} & -\frac{13}{16} & -\frac{33}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{1}{8} \\
+ \frac{11}{8} \\
+ \frac{43}{16} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{4} & \frac{1}{8} & -\frac{1}{8} \\
+ -\frac{13}{8} & -\frac{1}{16} & -\frac{21}{16} \\
+ -\frac{31}{16} & -\frac{13}{16} & -\frac{33}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{1}{8} \\
+ \frac{11}{8} \\
+ \frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{4} & \frac{1}{8} & -\frac{1}{8} \\
+ -\frac{13}{8} & -\frac{1}{16} & -\frac{21}{16} \\
+ -\frac{31}{16} & -\frac{13}{16} & -\frac{33}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{1}{8} \\
+ \frac{11}{8} \\
+ \frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{5}{4\ 8}+\frac{11}{8\ 8}+\frac{1}{8} \left(-\frac{43}{16}\right)=-\frac{1}{128}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{4} & \frac{1}{8} & -\frac{1}{8} \\
+ -\frac{13}{8} & -\frac{1}{16} & -\frac{21}{16} \\
+ -\frac{31}{16} & -\frac{13}{16} & -\frac{33}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{1}{8} \\
+ \frac{11}{8} \\
+ \frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$-\frac{1}{128}$} \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{4} & \frac{1}{8} & -\frac{1}{8} \\
+ -\frac{13}{8} & -\frac{1}{16} & -\frac{21}{16} \\
+ -\frac{31}{16} & -\frac{13}{16} & -\frac{33}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{1}{8} \\
+ \frac{11}{8} \\
+ \frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ -\frac{1}{128} \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{13}{8}\right)\, \times \, \frac{1}{8}+\frac{1}{16} \left(-\frac{11}{8}\right)+\left(-\frac{21}{16}\right)\, \times \, \frac{43}{16}=-\frac{977}{256}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{4} & \frac{1}{8} & -\frac{1}{8} \\
+ -\frac{13}{8} & -\frac{1}{16} & -\frac{21}{16} \\
+ -\frac{31}{16} & -\frac{13}{16} & -\frac{33}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{1}{8} \\
+ \frac{11}{8} \\
+ \frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ -\frac{1}{128} \\
+ \fbox{$-\frac{977}{256}$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{4} & \frac{1}{8} & -\frac{1}{8} \\
+ -\frac{13}{8} & -\frac{1}{16} & -\frac{21}{16} \\
+ -\frac{31}{16} & -\frac{13}{16} & -\frac{33}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{1}{8} \\
+ \frac{11}{8} \\
+ \frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ -\frac{1}{128} \\
+ -\frac{977}{256} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{31}{16}\right)\, \times \, \frac{1}{8}+\left(-\frac{13}{16}\right)\, \times \, \frac{11}{8}+\left(-\frac{33}{16}\right)\, \times \, \frac{43}{16}=-\frac{1767}{256}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ \frac{5}{4} & \frac{1}{8} & -\frac{1}{8} \\
+ -\frac{13}{8} & -\frac{1}{16} & -\frac{21}{16} \\
+ -\frac{31}{16} & -\frac{13}{16} & -\frac{33}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{1}{8} \\
+ \frac{11}{8} \\
+ \frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ -\frac{1}{128} \\
+ -\frac{977}{256} \\
+ \fbox{$-\frac{1767}{256}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/1426.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/1426.txt
new file mode 100644
index 0000000000000000000000000000000000000000..59fd551930671676ee66d72da530655181fbc167
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/1426.txt
@@ -0,0 +1,362 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ -\frac{19}{8} & 2 & \frac{3}{8} \\
+ -\frac{1}{2} & \frac{37}{16} & -\frac{21}{16} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ -\frac{7}{8} & \frac{7}{4} & \frac{11}{16} \\
+ -\frac{11}{4} & -\frac{11}{16} & \frac{7}{4} \\
+ 0 & -\frac{27}{16} & \frac{17}{8} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{19}{8} & 2 & \frac{3}{8} \\
+ -\frac{1}{2} & \frac{37}{16} & -\frac{21}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{7}{8} & \frac{7}{4} & \frac{11}{16} \\
+ -\frac{11}{4} & -\frac{11}{16} & \frac{7}{4} \\
+ 0 & -\frac{27}{16} & \frac{17}{8} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{19}{8} & 2 & \frac{3}{8} \\
+ -\frac{1}{2} & \frac{37}{16} & -\frac{21}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{7}{8} & \frac{7}{4} & \frac{11}{16} \\
+ -\frac{11}{4} & -\frac{11}{16} & \frac{7}{4} \\
+ 0 & -\frac{27}{16} & \frac{17}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{19}{8} & 2 & \frac{3}{8} \\
+ -\frac{1}{2} & \frac{37}{16} & -\frac{21}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{7}{8} & \frac{7}{4} & \frac{11}{16} \\
+ -\frac{11}{4} & -\frac{11}{16} & \frac{7}{4} \\
+ 0 & -\frac{27}{16} & \frac{17}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{19}{8}\right)\, \left(-\frac{7}{8}\right)+\frac{2 (-11)}{4}+\frac{3\ 0}{8}=-\frac{219}{64}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{19}{8} & 2 & \frac{3}{8} \\
+ -\frac{1}{2} & \frac{37}{16} & -\frac{21}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{7}{8} & \frac{7}{4} & \frac{11}{16} \\
+ -\frac{11}{4} & -\frac{11}{16} & \frac{7}{4} \\
+ 0 & -\frac{27}{16} & \frac{17}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$-\frac{219}{64}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{19}{8} & 2 & \frac{3}{8} \\
+ -\frac{1}{2} & \frac{37}{16} & -\frac{21}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{7}{8} & \frac{7}{4} & \frac{11}{16} \\
+ -\frac{11}{4} & -\frac{11}{16} & \frac{7}{4} \\
+ 0 & -\frac{27}{16} & \frac{17}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{219}{64} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{19}{8}\right)\, \times \, \frac{7}{4}+\frac{2 (-11)}{16}+\frac{3 (-27)}{8\ 16}=-\frac{789}{128}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{19}{8} & 2 & \frac{3}{8} \\
+ -\frac{1}{2} & \frac{37}{16} & -\frac{21}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{7}{8} & \frac{7}{4} & \frac{11}{16} \\
+ -\frac{11}{4} & -\frac{11}{16} & \frac{7}{4} \\
+ 0 & -\frac{27}{16} & \frac{17}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{219}{64} & \fbox{$-\frac{789}{128}$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{19}{8} & 2 & \frac{3}{8} \\
+ -\frac{1}{2} & \frac{37}{16} & -\frac{21}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{7}{8} & \frac{7}{4} & \frac{11}{16} \\
+ -\frac{11}{4} & -\frac{11}{16} & \frac{7}{4} \\
+ 0 & -\frac{27}{16} & \frac{17}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{219}{64} & -\frac{789}{128} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{19}{8}\right)\, \times \, \frac{11}{16}+\frac{2\ 7}{4}+\frac{3\ 17}{8\ 8}=\frac{341}{128}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{19}{8} & 2 & \frac{3}{8} \\
+ -\frac{1}{2} & \frac{37}{16} & -\frac{21}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{7}{8} & \frac{7}{4} & \frac{11}{16} \\
+ -\frac{11}{4} & -\frac{11}{16} & \frac{7}{4} \\
+ 0 & -\frac{27}{16} & \frac{17}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{219}{64} & -\frac{789}{128} & \fbox{$\frac{341}{128}$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{19}{8} & 2 & \frac{3}{8} \\
+ -\frac{1}{2} & \frac{37}{16} & -\frac{21}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{7}{8} & \frac{7}{4} & \frac{11}{16} \\
+ -\frac{11}{4} & -\frac{11}{16} & \frac{7}{4} \\
+ 0 & -\frac{27}{16} & \frac{17}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{219}{64} & -\frac{789}{128} & \frac{341}{128} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{7}{8\ 2}+\frac{37 (-11)}{16\ 4}+\left(-\frac{21}{16}\right)\, \times \, 0=-\frac{379}{64}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{19}{8} & 2 & \frac{3}{8} \\
+ -\frac{1}{2} & \frac{37}{16} & -\frac{21}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{7}{8} & \frac{7}{4} & \frac{11}{16} \\
+ -\frac{11}{4} & -\frac{11}{16} & \frac{7}{4} \\
+ 0 & -\frac{27}{16} & \frac{17}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{219}{64} & -\frac{789}{128} & \frac{341}{128} \\
+ \fbox{$-\frac{379}{64}$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{19}{8} & 2 & \frac{3}{8} \\
+ -\frac{1}{2} & \frac{37}{16} & -\frac{21}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{7}{8} & \frac{7}{4} & \frac{11}{16} \\
+ -\frac{11}{4} & -\frac{11}{16} & \frac{7}{4} \\
+ 0 & -\frac{27}{16} & \frac{17}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{219}{64} & -\frac{789}{128} & \frac{341}{128} \\
+ -\frac{379}{64} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{2} \left(-\frac{7}{4}\right)+\frac{37 (-11)}{16\ 16}+\left(-\frac{21}{16}\right)\, \left(-\frac{27}{16}\right)=-\frac{1}{4}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{19}{8} & 2 & \frac{3}{8} \\
+ -\frac{1}{2} & \frac{37}{16} & -\frac{21}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{7}{8} & \frac{7}{4} & \frac{11}{16} \\
+ -\frac{11}{4} & -\frac{11}{16} & \frac{7}{4} \\
+ 0 & -\frac{27}{16} & \frac{17}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{219}{64} & -\frac{789}{128} & \frac{341}{128} \\
+ -\frac{379}{64} & \fbox{$-\frac{1}{4}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{19}{8} & 2 & \frac{3}{8} \\
+ -\frac{1}{2} & \frac{37}{16} & -\frac{21}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{7}{8} & \frac{7}{4} & \frac{11}{16} \\
+ -\frac{11}{4} & -\frac{11}{16} & \frac{7}{4} \\
+ 0 & -\frac{27}{16} & \frac{17}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{219}{64} & -\frac{789}{128} & \frac{341}{128} \\
+ -\frac{379}{64} & -\frac{1}{4} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{2} \left(-\frac{11}{16}\right)+\frac{37\ 7}{16\ 4}+\left(-\frac{21}{16}\right)\, \times \, \frac{17}{8}=\frac{117}{128}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ -\frac{19}{8} & 2 & \frac{3}{8} \\
+ -\frac{1}{2} & \frac{37}{16} & -\frac{21}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{7}{8} & \frac{7}{4} & \frac{11}{16} \\
+ -\frac{11}{4} & -\frac{11}{16} & \frac{7}{4} \\
+ 0 & -\frac{27}{16} & \frac{17}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{219}{64} & -\frac{789}{128} & \frac{341}{128} \\
+ -\frac{379}{64} & -\frac{1}{4} & \fbox{$\frac{117}{128}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/1484.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/1484.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5fb148908fd63ed4bfc78ab7640617169d61c4d0
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/1484.txt
@@ -0,0 +1,159 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ 0 & 1 \\
+ 2 & 0 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -2 \\
+ -1 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ 0 & 1 \\
+ 2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -2 \\
+ -1 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 0 & 1 \\
+ 2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -2 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 0 & 1 \\
+ 2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -2 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0 (-2)+1 (-1)=-1. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 0 & 1 \\
+ 2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -2 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$-1$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 0 & 1 \\
+ 2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -2 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ -1 \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2 (-2)+0 (-1)=-4. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ 0 & 1 \\
+ 2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -2 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ -1 \\
+ \fbox{$-4$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/1489.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/1489.txt
new file mode 100644
index 0000000000000000000000000000000000000000..09efbbdd92d1555a41e71217997887f20924df87
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/1489.txt
@@ -0,0 +1,347 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ -2 & 0 \\
+ 2 & 2 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ -1 & 1 & -2 \\
+ 2 & 3 & 2 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ -2 & 0 \\
+ 2 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & 1 & -2 \\
+ 2 & 3 & 2 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -2 & 0 \\
+ 2 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & 1 & -2 \\
+ 2 & 3 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -2 & 0 \\
+ 2 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & 1 & -2 \\
+ 2 & 3 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, (-1)+0\ 2=2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -2 & 0 \\
+ 2 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & 1 & -2 \\
+ 2 & 3 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$2$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -2 & 0 \\
+ 2 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & 1 & -2 \\
+ 2 & 3 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 2 & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, \times \, 1+0\ 3=-2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -2 & 0 \\
+ 2 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & 1 & -2 \\
+ 2 & 3 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 2 & \fbox{$-2$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -2 & 0 \\
+ 2 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & 1 & -2 \\
+ 2 & 3 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 2 & -2 & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, (-2)+0\ 2=4. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -2 & 0 \\
+ 2 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & 1 & -2 \\
+ 2 & 3 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 2 & -2 & \fbox{$4$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -2 & 0 \\
+ 2 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & 1 & -2 \\
+ 2 & 3 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 2 & -2 & 4 \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2 (-1)+2\ 2=2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -2 & 0 \\
+ 2 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & 1 & -2 \\
+ 2 & 3 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 2 & -2 & 4 \\
+ \fbox{$2$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -2 & 0 \\
+ 2 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & 1 & -2 \\
+ 2 & 3 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 2 & -2 & 4 \\
+ 2 & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2\ 1+2\ 3=8. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -2 & 0 \\
+ 2 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & 1 & -2 \\
+ 2 & 3 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 2 & -2 & 4 \\
+ 2 & \fbox{$8$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -2 & 0 \\
+ 2 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & 1 & -2 \\
+ 2 & 3 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 2 & -2 & 4 \\
+ 2 & 8 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2 (-2)+2\ 2=0. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ -2 & 0 \\
+ 2 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & 1 & -2 \\
+ 2 & 3 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 2 & -2 & 4 \\
+ 2 & 8 & \fbox{$0$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/152.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/152.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bf46b5aac4168cffd651711da57ff99fd6cf54cd
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/152.txt
@@ -0,0 +1,166 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ \frac{21}{10} & -\frac{3}{5} & \frac{3}{5} \\
+ -\frac{19}{10} & \frac{17}{10} & -\frac{21}{10} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ \frac{12}{5} \\
+ -\frac{1}{5} \\
+ -\frac{12}{5} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{21}{10} & -\frac{3}{5} & \frac{3}{5} \\
+ -\frac{19}{10} & \frac{17}{10} & -\frac{21}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{12}{5} \\
+ -\frac{1}{5} \\
+ -\frac{12}{5} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{21}{10} & -\frac{3}{5} & \frac{3}{5} \\
+ -\frac{19}{10} & \frac{17}{10} & -\frac{21}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{12}{5} \\
+ -\frac{1}{5} \\
+ -\frac{12}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{21}{10} & -\frac{3}{5} & \frac{3}{5} \\
+ -\frac{19}{10} & \frac{17}{10} & -\frac{21}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{12}{5} \\
+ -\frac{1}{5} \\
+ -\frac{12}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{21\ 12}{10\ 5}+\frac{3}{5\ 5}+\frac{3 (-12)}{5\ 5}=\frac{93}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{21}{10} & -\frac{3}{5} & \frac{3}{5} \\
+ -\frac{19}{10} & \frac{17}{10} & -\frac{21}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{12}{5} \\
+ -\frac{1}{5} \\
+ -\frac{12}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$\frac{93}{25}$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{21}{10} & -\frac{3}{5} & \frac{3}{5} \\
+ -\frac{19}{10} & \frac{17}{10} & -\frac{21}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{12}{5} \\
+ -\frac{1}{5} \\
+ -\frac{12}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \frac{93}{25} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{19}{10}\right)\, \times \, \frac{12}{5}+\frac{1}{5} \left(-\frac{17}{10}\right)+\left(-\frac{21}{10}\right)\, \left(-\frac{12}{5}\right)=\frac{7}{50}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ \frac{21}{10} & -\frac{3}{5} & \frac{3}{5} \\
+ -\frac{19}{10} & \frac{17}{10} & -\frac{21}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{12}{5} \\
+ -\frac{1}{5} \\
+ -\frac{12}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \frac{93}{25} \\
+ \fbox{$\frac{7}{50}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/1628.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/1628.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b82f8b5a0ef808b8f17aacfea75fe2406cbfe87d
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/1628.txt
@@ -0,0 +1,362 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ -3 & 0 & -\frac{7}{3} \\
+ \frac{5}{3} & \frac{5}{3} & -\frac{8}{3} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ -\frac{5}{3} & -2 & \frac{2}{3} \\
+ 2 & -\frac{4}{3} & -\frac{4}{3} \\
+ 0 & 2 & -1 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ -3 & 0 & -\frac{7}{3} \\
+ \frac{5}{3} & \frac{5}{3} & -\frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{5}{3} & -2 & \frac{2}{3} \\
+ 2 & -\frac{4}{3} & -\frac{4}{3} \\
+ 0 & 2 & -1 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -3 & 0 & -\frac{7}{3} \\
+ \frac{5}{3} & \frac{5}{3} & -\frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{5}{3} & -2 & \frac{2}{3} \\
+ 2 & -\frac{4}{3} & -\frac{4}{3} \\
+ 0 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -3 & 0 & -\frac{7}{3} \\
+ \frac{5}{3} & \frac{5}{3} & -\frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{5}{3} & -2 & \frac{2}{3} \\
+ 2 & -\frac{4}{3} & -\frac{4}{3} \\
+ 0 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-3)\, \left(-\frac{5}{3}\right)+0\ 2+\left(-\frac{7}{3}\right)\, \times \, 0=5. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -3 & 0 & -\frac{7}{3} \\
+ \frac{5}{3} & \frac{5}{3} & -\frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{5}{3} & -2 & \frac{2}{3} \\
+ 2 & -\frac{4}{3} & -\frac{4}{3} \\
+ 0 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$5$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -3 & 0 & -\frac{7}{3} \\
+ \frac{5}{3} & \frac{5}{3} & -\frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{5}{3} & -2 & \frac{2}{3} \\
+ 2 & -\frac{4}{3} & -\frac{4}{3} \\
+ 0 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 5 & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-3)\, (-2)+\frac{0 (-4)}{3}+\left(-\frac{7}{3}\right)\, \times \, 2=\frac{4}{3}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -3 & 0 & -\frac{7}{3} \\
+ \frac{5}{3} & \frac{5}{3} & -\frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{5}{3} & -2 & \frac{2}{3} \\
+ 2 & -\frac{4}{3} & -\frac{4}{3} \\
+ 0 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 5 & \fbox{$\frac{4}{3}$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -3 & 0 & -\frac{7}{3} \\
+ \frac{5}{3} & \frac{5}{3} & -\frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{5}{3} & -2 & \frac{2}{3} \\
+ 2 & -\frac{4}{3} & -\frac{4}{3} \\
+ 0 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 5 & \frac{4}{3} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-3)\, \times \, \frac{2}{3}+\frac{0 (-4)}{3}+\left(-\frac{7}{3}\right)\, (-1)=\frac{1}{3}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -3 & 0 & -\frac{7}{3} \\
+ \frac{5}{3} & \frac{5}{3} & -\frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{5}{3} & -2 & \frac{2}{3} \\
+ 2 & -\frac{4}{3} & -\frac{4}{3} \\
+ 0 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 5 & \frac{4}{3} & \fbox{$\frac{1}{3}$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -3 & 0 & -\frac{7}{3} \\
+ \frac{5}{3} & \frac{5}{3} & -\frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{5}{3} & -2 & \frac{2}{3} \\
+ 2 & -\frac{4}{3} & -\frac{4}{3} \\
+ 0 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 5 & \frac{4}{3} & \frac{1}{3} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{5 (-5)}{3\ 3}+\frac{5\ 2}{3}+\left(-\frac{8}{3}\right)\, \times \, 0=\frac{5}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -3 & 0 & -\frac{7}{3} \\
+ \frac{5}{3} & \frac{5}{3} & -\frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{5}{3} & -2 & \frac{2}{3} \\
+ 2 & -\frac{4}{3} & -\frac{4}{3} \\
+ 0 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 5 & \frac{4}{3} & \frac{1}{3} \\
+ \fbox{$\frac{5}{9}$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -3 & 0 & -\frac{7}{3} \\
+ \frac{5}{3} & \frac{5}{3} & -\frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{5}{3} & -2 & \frac{2}{3} \\
+ 2 & -\frac{4}{3} & -\frac{4}{3} \\
+ 0 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 5 & \frac{4}{3} & \frac{1}{3} \\
+ \frac{5}{9} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{5 (-2)}{3}+\frac{5 (-4)}{3\ 3}+\left(-\frac{8}{3}\right)\, \times \, 2=-\frac{98}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -3 & 0 & -\frac{7}{3} \\
+ \frac{5}{3} & \frac{5}{3} & -\frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{5}{3} & -2 & \frac{2}{3} \\
+ 2 & -\frac{4}{3} & -\frac{4}{3} \\
+ 0 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 5 & \frac{4}{3} & \frac{1}{3} \\
+ \frac{5}{9} & \fbox{$-\frac{98}{9}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -3 & 0 & -\frac{7}{3} \\
+ \frac{5}{3} & \frac{5}{3} & -\frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{5}{3} & -2 & \frac{2}{3} \\
+ 2 & -\frac{4}{3} & -\frac{4}{3} \\
+ 0 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 5 & \frac{4}{3} & \frac{1}{3} \\
+ \frac{5}{9} & -\frac{98}{9} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{5\ 2}{3\ 3}+\frac{5 (-4)}{3\ 3}+\left(-\frac{8}{3}\right)\, (-1)=\frac{14}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ -3 & 0 & -\frac{7}{3} \\
+ \frac{5}{3} & \frac{5}{3} & -\frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{5}{3} & -2 & \frac{2}{3} \\
+ 2 & -\frac{4}{3} & -\frac{4}{3} \\
+ 0 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 5 & \frac{4}{3} & \frac{1}{3} \\
+ \frac{5}{9} & -\frac{98}{9} & \fbox{$\frac{14}{9}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/1784.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/1784.txt
new file mode 100644
index 0000000000000000000000000000000000000000..45860d1d2e5f3296eba478f4ac5d58b6c760b615
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/1784.txt
@@ -0,0 +1,375 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ -\frac{9}{5} & -\frac{14}{5} \\
+ -\frac{14}{5} & \frac{6}{5} \\
+ -\frac{3}{5} & \frac{8}{5} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{cc}
+ \frac{2}{5} & -\frac{11}{5} \\
+ -\frac{3}{5} & -2 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{9}{5} & -\frac{14}{5} \\
+ -\frac{14}{5} & \frac{6}{5} \\
+ -\frac{3}{5} & \frac{8}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{2}{5} & -\frac{11}{5} \\
+ -\frac{3}{5} & -2 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 2. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 2: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{9}{5} & -\frac{14}{5} \\
+ -\frac{14}{5} & \frac{6}{5} \\
+ -\frac{3}{5} & \frac{8}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{2}{5} & -\frac{11}{5} \\
+ -\frac{3}{5} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{9}{5} & -\frac{14}{5} \\
+ -\frac{14}{5} & \frac{6}{5} \\
+ -\frac{3}{5} & \frac{8}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{2}{5} & -\frac{11}{5} \\
+ -\frac{3}{5} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{9}{5}\right)\, \times \, \frac{2}{5}+\left(-\frac{14}{5}\right)\, \left(-\frac{3}{5}\right)=\frac{24}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{9}{5} & -\frac{14}{5} \\
+ -\frac{14}{5} & \frac{6}{5} \\
+ -\frac{3}{5} & \frac{8}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{2}{5} & -\frac{11}{5} \\
+ -\frac{3}{5} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \fbox{$\frac{24}{25}$} & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{9}{5} & -\frac{14}{5} \\
+ -\frac{14}{5} & \frac{6}{5} \\
+ -\frac{3}{5} & \frac{8}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{2}{5} & -\frac{11}{5} \\
+ -\frac{3}{5} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{24}{25} & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{9}{5}\right)\, \left(-\frac{11}{5}\right)+\left(-\frac{14}{5}\right)\, (-2)=\frac{239}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{9}{5} & -\frac{14}{5} \\
+ -\frac{14}{5} & \frac{6}{5} \\
+ -\frac{3}{5} & \frac{8}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{2}{5} & -\frac{11}{5} \\
+ -\frac{3}{5} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{24}{25} & \fbox{$\frac{239}{25}$} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{9}{5} & -\frac{14}{5} \\
+ -\frac{14}{5} & \frac{6}{5} \\
+ -\frac{3}{5} & \frac{8}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{2}{5} & -\frac{11}{5} \\
+ -\frac{3}{5} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{24}{25} & \frac{239}{25} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{14}{5}\right)\, \times \, \frac{2}{5}+\frac{6 (-3)}{5\ 5}=-\frac{46}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{9}{5} & -\frac{14}{5} \\
+ -\frac{14}{5} & \frac{6}{5} \\
+ -\frac{3}{5} & \frac{8}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{2}{5} & -\frac{11}{5} \\
+ -\frac{3}{5} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{24}{25} & \frac{239}{25} \\
+ \fbox{$-\frac{46}{25}$} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{9}{5} & -\frac{14}{5} \\
+ -\frac{14}{5} & \frac{6}{5} \\
+ -\frac{3}{5} & \frac{8}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{2}{5} & -\frac{11}{5} \\
+ -\frac{3}{5} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{24}{25} & \frac{239}{25} \\
+ -\frac{46}{25} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{14}{5}\right)\, \left(-\frac{11}{5}\right)+\frac{6 (-2)}{5}=\frac{94}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{9}{5} & -\frac{14}{5} \\
+ -\frac{14}{5} & \frac{6}{5} \\
+ -\frac{3}{5} & \frac{8}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{2}{5} & -\frac{11}{5} \\
+ -\frac{3}{5} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{24}{25} & \frac{239}{25} \\
+ -\frac{46}{25} & \fbox{$\frac{94}{25}$} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{9}{5} & -\frac{14}{5} \\
+ -\frac{14}{5} & \frac{6}{5} \\
+ -\frac{3}{5} & \frac{8}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{2}{5} & -\frac{11}{5} \\
+ -\frac{3}{5} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{24}{25} & \frac{239}{25} \\
+ -\frac{46}{25} & \frac{94}{25} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{3}{5}\right)\, \times \, \frac{2}{5}+\frac{8 (-3)}{5\ 5}=-\frac{6}{5}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{9}{5} & -\frac{14}{5} \\
+ -\frac{14}{5} & \frac{6}{5} \\
+ -\frac{3}{5} & \frac{8}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{2}{5} & -\frac{11}{5} \\
+ -\frac{3}{5} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{24}{25} & \frac{239}{25} \\
+ -\frac{46}{25} & \frac{94}{25} \\
+ \fbox{$-\frac{6}{5}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{9}{5} & -\frac{14}{5} \\
+ -\frac{14}{5} & \frac{6}{5} \\
+ -\frac{3}{5} & \frac{8}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{2}{5} & -\frac{11}{5} \\
+ -\frac{3}{5} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{24}{25} & \frac{239}{25} \\
+ -\frac{46}{25} & \frac{94}{25} \\
+ -\frac{6}{5} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{3}{5}\right)\, \left(-\frac{11}{5}\right)+\frac{8 (-2)}{5}=-\frac{47}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ -\frac{9}{5} & -\frac{14}{5} \\
+ -\frac{14}{5} & \frac{6}{5} \\
+ -\frac{3}{5} & \frac{8}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{2}{5} & -\frac{11}{5} \\
+ -\frac{3}{5} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{24}{25} & \frac{239}{25} \\
+ -\frac{46}{25} & \frac{94}{25} \\
+ -\frac{6}{5} & \fbox{$-\frac{47}{25}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/1787.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/1787.txt
new file mode 100644
index 0000000000000000000000000000000000000000..faee2f58590f2fb6a7b17256a4ea5bb8b54685fe
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/1787.txt
@@ -0,0 +1,528 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ -\frac{7}{8} & \frac{23}{8} \\
+ -\frac{5}{2} & -\frac{31}{16} \\
+ -\frac{1}{8} & -\frac{13}{8} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ \frac{11}{4} & \frac{15}{8} & \frac{37}{16} \\
+ \frac{19}{8} & -\frac{11}{16} & -\frac{43}{16} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{7}{8} & \frac{23}{8} \\
+ -\frac{5}{2} & -\frac{31}{16} \\
+ -\frac{1}{8} & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{11}{4} & \frac{15}{8} & \frac{37}{16} \\
+ \frac{19}{8} & -\frac{11}{16} & -\frac{43}{16} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{7}{8} & \frac{23}{8} \\
+ -\frac{5}{2} & -\frac{31}{16} \\
+ -\frac{1}{8} & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{11}{4} & \frac{15}{8} & \frac{37}{16} \\
+ \frac{19}{8} & -\frac{11}{16} & -\frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{7}{8} & \frac{23}{8} \\
+ -\frac{5}{2} & -\frac{31}{16} \\
+ -\frac{1}{8} & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{11}{4} & \frac{15}{8} & \frac{37}{16} \\
+ \frac{19}{8} & -\frac{11}{16} & -\frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{7}{8}\right)\, \times \, \frac{11}{4}+\frac{23\ 19}{8\ 8}=\frac{283}{64}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{7}{8} & \frac{23}{8} \\
+ -\frac{5}{2} & -\frac{31}{16} \\
+ -\frac{1}{8} & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{11}{4} & \frac{15}{8} & \frac{37}{16} \\
+ \frac{19}{8} & -\frac{11}{16} & -\frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$\frac{283}{64}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{7}{8} & \frac{23}{8} \\
+ -\frac{5}{2} & -\frac{31}{16} \\
+ -\frac{1}{8} & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{11}{4} & \frac{15}{8} & \frac{37}{16} \\
+ \frac{19}{8} & -\frac{11}{16} & -\frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{283}{64} & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{7}{8}\right)\, \times \, \frac{15}{8}+\frac{23 (-11)}{8\ 16}=-\frac{463}{128}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{7}{8} & \frac{23}{8} \\
+ -\frac{5}{2} & -\frac{31}{16} \\
+ -\frac{1}{8} & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{11}{4} & \frac{15}{8} & \frac{37}{16} \\
+ \frac{19}{8} & -\frac{11}{16} & -\frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{283}{64} & \fbox{$-\frac{463}{128}$} & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{7}{8} & \frac{23}{8} \\
+ -\frac{5}{2} & -\frac{31}{16} \\
+ -\frac{1}{8} & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{11}{4} & \frac{15}{8} & \frac{37}{16} \\
+ \frac{19}{8} & -\frac{11}{16} & -\frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{283}{64} & -\frac{463}{128} & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{7}{8}\right)\, \times \, \frac{37}{16}+\frac{23 (-43)}{8\ 16}=-\frac{39}{4}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{7}{8} & \frac{23}{8} \\
+ -\frac{5}{2} & -\frac{31}{16} \\
+ -\frac{1}{8} & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{11}{4} & \frac{15}{8} & \frac{37}{16} \\
+ \frac{19}{8} & -\frac{11}{16} & -\frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{283}{64} & -\frac{463}{128} & \fbox{$-\frac{39}{4}$} \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{7}{8} & \frac{23}{8} \\
+ -\frac{5}{2} & -\frac{31}{16} \\
+ -\frac{1}{8} & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{11}{4} & \frac{15}{8} & \frac{37}{16} \\
+ \frac{19}{8} & -\frac{11}{16} & -\frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{283}{64} & -\frac{463}{128} & -\frac{39}{4} \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{5}{2}\right)\, \times \, \frac{11}{4}+\left(-\frac{31}{16}\right)\, \times \, \frac{19}{8}=-\frac{1469}{128}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{7}{8} & \frac{23}{8} \\
+ -\frac{5}{2} & -\frac{31}{16} \\
+ -\frac{1}{8} & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{11}{4} & \frac{15}{8} & \frac{37}{16} \\
+ \frac{19}{8} & -\frac{11}{16} & -\frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{283}{64} & -\frac{463}{128} & -\frac{39}{4} \\
+ \fbox{$-\frac{1469}{128}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{7}{8} & \frac{23}{8} \\
+ -\frac{5}{2} & -\frac{31}{16} \\
+ -\frac{1}{8} & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{11}{4} & \frac{15}{8} & \frac{37}{16} \\
+ \frac{19}{8} & -\frac{11}{16} & -\frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{283}{64} & -\frac{463}{128} & -\frac{39}{4} \\
+ -\frac{1469}{128} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{5}{2}\right)\, \times \, \frac{15}{8}+\left(-\frac{31}{16}\right)\, \left(-\frac{11}{16}\right)=-\frac{859}{256}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{7}{8} & \frac{23}{8} \\
+ -\frac{5}{2} & -\frac{31}{16} \\
+ -\frac{1}{8} & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{11}{4} & \frac{15}{8} & \frac{37}{16} \\
+ \frac{19}{8} & -\frac{11}{16} & -\frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{283}{64} & -\frac{463}{128} & -\frac{39}{4} \\
+ -\frac{1469}{128} & \fbox{$-\frac{859}{256}$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{7}{8} & \frac{23}{8} \\
+ -\frac{5}{2} & -\frac{31}{16} \\
+ -\frac{1}{8} & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{11}{4} & \frac{15}{8} & \frac{37}{16} \\
+ \frac{19}{8} & -\frac{11}{16} & -\frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{283}{64} & -\frac{463}{128} & -\frac{39}{4} \\
+ -\frac{1469}{128} & -\frac{859}{256} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{5}{2}\right)\, \times \, \frac{37}{16}+\left(-\frac{31}{16}\right)\, \left(-\frac{43}{16}\right)=-\frac{147}{256}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{7}{8} & \frac{23}{8} \\
+ -\frac{5}{2} & -\frac{31}{16} \\
+ -\frac{1}{8} & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{11}{4} & \frac{15}{8} & \frac{37}{16} \\
+ \frac{19}{8} & -\frac{11}{16} & -\frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{283}{64} & -\frac{463}{128} & -\frac{39}{4} \\
+ -\frac{1469}{128} & -\frac{859}{256} & \fbox{$-\frac{147}{256}$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{7}{8} & \frac{23}{8} \\
+ -\frac{5}{2} & -\frac{31}{16} \\
+ -\frac{1}{8} & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{11}{4} & \frac{15}{8} & \frac{37}{16} \\
+ \frac{19}{8} & -\frac{11}{16} & -\frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{283}{64} & -\frac{463}{128} & -\frac{39}{4} \\
+ -\frac{1469}{128} & -\frac{859}{256} & -\frac{147}{256} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{8} \left(-\frac{11}{4}\right)+\left(-\frac{13}{8}\right)\, \times \, \frac{19}{8}=-\frac{269}{64}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{7}{8} & \frac{23}{8} \\
+ -\frac{5}{2} & -\frac{31}{16} \\
+ -\frac{1}{8} & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{11}{4} & \frac{15}{8} & \frac{37}{16} \\
+ \frac{19}{8} & -\frac{11}{16} & -\frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{283}{64} & -\frac{463}{128} & -\frac{39}{4} \\
+ -\frac{1469}{128} & -\frac{859}{256} & -\frac{147}{256} \\
+ \fbox{$-\frac{269}{64}$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{7}{8} & \frac{23}{8} \\
+ -\frac{5}{2} & -\frac{31}{16} \\
+ -\frac{1}{8} & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{11}{4} & \frac{15}{8} & \frac{37}{16} \\
+ \frac{19}{8} & -\frac{11}{16} & -\frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{283}{64} & -\frac{463}{128} & -\frac{39}{4} \\
+ -\frac{1469}{128} & -\frac{859}{256} & -\frac{147}{256} \\
+ -\frac{269}{64} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{8} \left(-\frac{15}{8}\right)+\left(-\frac{13}{8}\right)\, \left(-\frac{11}{16}\right)=\frac{113}{128}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{7}{8} & \frac{23}{8} \\
+ -\frac{5}{2} & -\frac{31}{16} \\
+ -\frac{1}{8} & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{11}{4} & \frac{15}{8} & \frac{37}{16} \\
+ \frac{19}{8} & -\frac{11}{16} & -\frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{283}{64} & -\frac{463}{128} & -\frac{39}{4} \\
+ -\frac{1469}{128} & -\frac{859}{256} & -\frac{147}{256} \\
+ -\frac{269}{64} & \fbox{$\frac{113}{128}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{7}{8} & \frac{23}{8} \\
+ -\frac{5}{2} & -\frac{31}{16} \\
+ -\frac{1}{8} & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{11}{4} & \frac{15}{8} & \frac{37}{16} \\
+ \frac{19}{8} & -\frac{11}{16} & -\frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{283}{64} & -\frac{463}{128} & -\frac{39}{4} \\
+ -\frac{1469}{128} & -\frac{859}{256} & -\frac{147}{256} \\
+ -\frac{269}{64} & \frac{113}{128} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{8} \left(-\frac{37}{16}\right)+\left(-\frac{13}{8}\right)\, \left(-\frac{43}{16}\right)=\frac{261}{64}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ -\frac{7}{8} & \frac{23}{8} \\
+ -\frac{5}{2} & -\frac{31}{16} \\
+ -\frac{1}{8} & -\frac{13}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{11}{4} & \frac{15}{8} & \frac{37}{16} \\
+ \frac{19}{8} & -\frac{11}{16} & -\frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{283}{64} & -\frac{463}{128} & -\frac{39}{4} \\
+ -\frac{1469}{128} & -\frac{859}{256} & -\frac{147}{256} \\
+ -\frac{269}{64} & \frac{113}{128} & \fbox{$\frac{261}{64}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/1795.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/1795.txt
new file mode 100644
index 0000000000000000000000000000000000000000..46c12a3b2027002e2333304d038f4c927ae604e3
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/1795.txt
@@ -0,0 +1,549 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ 1 & \frac{1}{3} & -1 \\
+ -2 & 0 & -\frac{5}{6} \\
+ \frac{5}{2} & \frac{5}{6} & -\frac{1}{6} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ -\frac{1}{6} & -\frac{5}{2} & -2 \\
+ \frac{3}{2} & 0 & \frac{5}{2} \\
+ -1 & -2 & -\frac{11}{6} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ 1 & \frac{1}{3} & -1 \\
+ -2 & 0 & -\frac{5}{6} \\
+ \frac{5}{2} & \frac{5}{6} & -\frac{1}{6} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{6} & -\frac{5}{2} & -2 \\
+ \frac{3}{2} & 0 & \frac{5}{2} \\
+ -1 & -2 & -\frac{11}{6} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 1 & \frac{1}{3} & -1 \\
+ -2 & 0 & -\frac{5}{6} \\
+ \frac{5}{2} & \frac{5}{6} & -\frac{1}{6} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{6} & -\frac{5}{2} & -2 \\
+ \frac{3}{2} & 0 & \frac{5}{2} \\
+ -1 & -2 & -\frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 1 & \frac{1}{3} & -1 \\
+ -2 & 0 & -\frac{5}{6} \\
+ \frac{5}{2} & \frac{5}{6} & -\frac{1}{6} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{6} & -\frac{5}{2} & -2 \\
+ \frac{3}{2} & 0 & \frac{5}{2} \\
+ -1 & -2 & -\frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{6} (-1)+\frac{3}{3\ 2}+(-1)\, (-1)=\frac{4}{3}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 1 & \frac{1}{3} & -1 \\
+ -2 & 0 & -\frac{5}{6} \\
+ \frac{5}{2} & \frac{5}{6} & -\frac{1}{6} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{6} & -\frac{5}{2} & -2 \\
+ \frac{3}{2} & 0 & \frac{5}{2} \\
+ -1 & -2 & -\frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$\frac{4}{3}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 1 & \frac{1}{3} & -1 \\
+ -2 & 0 & -\frac{5}{6} \\
+ \frac{5}{2} & \frac{5}{6} & -\frac{1}{6} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{6} & -\frac{5}{2} & -2 \\
+ \frac{3}{2} & 0 & \frac{5}{2} \\
+ -1 & -2 & -\frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{4}{3} & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }-\frac{5}{2}+\frac{0}{3}+(-1)\, (-2)=-\frac{1}{2}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 1 & \frac{1}{3} & -1 \\
+ -2 & 0 & -\frac{5}{6} \\
+ \frac{5}{2} & \frac{5}{6} & -\frac{1}{6} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{6} & -\frac{5}{2} & -2 \\
+ \frac{3}{2} & 0 & \frac{5}{2} \\
+ -1 & -2 & -\frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{4}{3} & \fbox{$-\frac{1}{2}$} & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 1 & \frac{1}{3} & -1 \\
+ -2 & 0 & -\frac{5}{6} \\
+ \frac{5}{2} & \frac{5}{6} & -\frac{1}{6} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{6} & -\frac{5}{2} & -2 \\
+ \frac{3}{2} & 0 & \frac{5}{2} \\
+ -1 & -2 & -\frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{4}{3} & -\frac{1}{2} & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1 (-2)+\frac{5}{3\ 2}+(-1)\, \left(-\frac{11}{6}\right)=\frac{2}{3}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 1 & \frac{1}{3} & -1 \\
+ -2 & 0 & -\frac{5}{6} \\
+ \frac{5}{2} & \frac{5}{6} & -\frac{1}{6} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{6} & -\frac{5}{2} & -2 \\
+ \frac{3}{2} & 0 & \frac{5}{2} \\
+ -1 & -2 & -\frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{4}{3} & -\frac{1}{2} & \fbox{$\frac{2}{3}$} \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 1 & \frac{1}{3} & -1 \\
+ -2 & 0 & -\frac{5}{6} \\
+ \frac{5}{2} & \frac{5}{6} & -\frac{1}{6} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{6} & -\frac{5}{2} & -2 \\
+ \frac{3}{2} & 0 & \frac{5}{2} \\
+ -1 & -2 & -\frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{4}{3} & -\frac{1}{2} & \frac{2}{3} \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2}{6}+\frac{0\ 3}{2}+\left(-\frac{5}{6}\right)\, (-1)=\frac{7}{6}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 1 & \frac{1}{3} & -1 \\
+ -2 & 0 & -\frac{5}{6} \\
+ \frac{5}{2} & \frac{5}{6} & -\frac{1}{6} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{6} & -\frac{5}{2} & -2 \\
+ \frac{3}{2} & 0 & \frac{5}{2} \\
+ -1 & -2 & -\frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{4}{3} & -\frac{1}{2} & \frac{2}{3} \\
+ \fbox{$\frac{7}{6}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 1 & \frac{1}{3} & -1 \\
+ -2 & 0 & -\frac{5}{6} \\
+ \frac{5}{2} & \frac{5}{6} & -\frac{1}{6} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{6} & -\frac{5}{2} & -2 \\
+ \frac{3}{2} & 0 & \frac{5}{2} \\
+ -1 & -2 & -\frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{4}{3} & -\frac{1}{2} & \frac{2}{3} \\
+ \frac{7}{6} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, \left(-\frac{5}{2}\right)+0\ 0+\left(-\frac{5}{6}\right)\, (-2)=\frac{20}{3}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 1 & \frac{1}{3} & -1 \\
+ -2 & 0 & -\frac{5}{6} \\
+ \frac{5}{2} & \frac{5}{6} & -\frac{1}{6} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{6} & -\frac{5}{2} & -2 \\
+ \frac{3}{2} & 0 & \frac{5}{2} \\
+ -1 & -2 & -\frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{4}{3} & -\frac{1}{2} & \frac{2}{3} \\
+ \frac{7}{6} & \fbox{$\frac{20}{3}$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 1 & \frac{1}{3} & -1 \\
+ -2 & 0 & -\frac{5}{6} \\
+ \frac{5}{2} & \frac{5}{6} & -\frac{1}{6} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{6} & -\frac{5}{2} & -2 \\
+ \frac{3}{2} & 0 & \frac{5}{2} \\
+ -1 & -2 & -\frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{4}{3} & -\frac{1}{2} & \frac{2}{3} \\
+ \frac{7}{6} & \frac{20}{3} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, (-2)+\frac{0\ 5}{2}+\left(-\frac{5}{6}\right)\, \left(-\frac{11}{6}\right)=\frac{199}{36}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 1 & \frac{1}{3} & -1 \\
+ -2 & 0 & -\frac{5}{6} \\
+ \frac{5}{2} & \frac{5}{6} & -\frac{1}{6} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{6} & -\frac{5}{2} & -2 \\
+ \frac{3}{2} & 0 & \frac{5}{2} \\
+ -1 & -2 & -\frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{4}{3} & -\frac{1}{2} & \frac{2}{3} \\
+ \frac{7}{6} & \frac{20}{3} & \fbox{$\frac{199}{36}$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 1 & \frac{1}{3} & -1 \\
+ -2 & 0 & -\frac{5}{6} \\
+ \frac{5}{2} & \frac{5}{6} & -\frac{1}{6} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{6} & -\frac{5}{2} & -2 \\
+ \frac{3}{2} & 0 & \frac{5}{2} \\
+ -1 & -2 & -\frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{4}{3} & -\frac{1}{2} & \frac{2}{3} \\
+ \frac{7}{6} & \frac{20}{3} & \frac{199}{36} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{6} \left(-\frac{5}{2}\right)+\frac{5\ 3}{6\ 2}+\frac{1}{6}=1. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 1 & \frac{1}{3} & -1 \\
+ -2 & 0 & -\frac{5}{6} \\
+ \frac{5}{2} & \frac{5}{6} & -\frac{1}{6} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{6} & -\frac{5}{2} & -2 \\
+ \frac{3}{2} & 0 & \frac{5}{2} \\
+ -1 & -2 & -\frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{4}{3} & -\frac{1}{2} & \frac{2}{3} \\
+ \frac{7}{6} & \frac{20}{3} & \frac{199}{36} \\
+ \fbox{$1$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 1 & \frac{1}{3} & -1 \\
+ -2 & 0 & -\frac{5}{6} \\
+ \frac{5}{2} & \frac{5}{6} & -\frac{1}{6} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{6} & -\frac{5}{2} & -2 \\
+ \frac{3}{2} & 0 & \frac{5}{2} \\
+ -1 & -2 & -\frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{4}{3} & -\frac{1}{2} & \frac{2}{3} \\
+ \frac{7}{6} & \frac{20}{3} & \frac{199}{36} \\
+ 1 & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{5 (-5)}{2\ 2}+\frac{5\ 0}{6}+\frac{2}{6}=-\frac{71}{12}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 1 & \frac{1}{3} & -1 \\
+ -2 & 0 & -\frac{5}{6} \\
+ \frac{5}{2} & \frac{5}{6} & -\frac{1}{6} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{6} & -\frac{5}{2} & -2 \\
+ \frac{3}{2} & 0 & \frac{5}{2} \\
+ -1 & -2 & -\frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{4}{3} & -\frac{1}{2} & \frac{2}{3} \\
+ \frac{7}{6} & \frac{20}{3} & \frac{199}{36} \\
+ 1 & \fbox{$-\frac{71}{12}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 1 & \frac{1}{3} & -1 \\
+ -2 & 0 & -\frac{5}{6} \\
+ \frac{5}{2} & \frac{5}{6} & -\frac{1}{6} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{6} & -\frac{5}{2} & -2 \\
+ \frac{3}{2} & 0 & \frac{5}{2} \\
+ -1 & -2 & -\frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{4}{3} & -\frac{1}{2} & \frac{2}{3} \\
+ \frac{7}{6} & \frac{20}{3} & \frac{199}{36} \\
+ 1 & -\frac{71}{12} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{5 (-2)}{2}+\frac{5\ 5}{6\ 2}+\frac{11}{6\ 6}=-\frac{47}{18}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ 1 & \frac{1}{3} & -1 \\
+ -2 & 0 & -\frac{5}{6} \\
+ \frac{5}{2} & \frac{5}{6} & -\frac{1}{6} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{6} & -\frac{5}{2} & -2 \\
+ \frac{3}{2} & 0 & \frac{5}{2} \\
+ -1 & -2 & -\frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{4}{3} & -\frac{1}{2} & \frac{2}{3} \\
+ \frac{7}{6} & \frac{20}{3} & \frac{199}{36} \\
+ 1 & -\frac{71}{12} & \fbox{$-\frac{47}{18}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/1831.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/1831.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7fdf53f46add8579f305963f5d4b31dc1dbd17d0
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/1831.txt
@@ -0,0 +1,222 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ \frac{2}{9} & -\frac{10}{9} \\
+ \frac{2}{3} & -\frac{7}{9} \\
+ -\frac{8}{9} & -\frac{8}{9} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ \frac{13}{9} \\
+ -\frac{8}{3} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ \frac{2}{9} & -\frac{10}{9} \\
+ \frac{2}{3} & -\frac{7}{9} \\
+ -\frac{8}{9} & -\frac{8}{9} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{13}{9} \\
+ -\frac{8}{3} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{2}{9} & -\frac{10}{9} \\
+ \frac{2}{3} & -\frac{7}{9} \\
+ -\frac{8}{9} & -\frac{8}{9} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{13}{9} \\
+ -\frac{8}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{2}{9} & -\frac{10}{9} \\
+ \frac{2}{3} & -\frac{7}{9} \\
+ -\frac{8}{9} & -\frac{8}{9} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{13}{9} \\
+ -\frac{8}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2\ 13}{9\ 9}+\left(-\frac{10}{9}\right)\, \left(-\frac{8}{3}\right)=\frac{266}{81}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{2}{9} & -\frac{10}{9} \\
+ \frac{2}{3} & -\frac{7}{9} \\
+ -\frac{8}{9} & -\frac{8}{9} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{13}{9} \\
+ -\frac{8}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$\frac{266}{81}$} \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{2}{9} & -\frac{10}{9} \\
+ \frac{2}{3} & -\frac{7}{9} \\
+ -\frac{8}{9} & -\frac{8}{9} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{13}{9} \\
+ -\frac{8}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \frac{266}{81} \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2\ 13}{3\ 9}+\left(-\frac{7}{9}\right)\, \left(-\frac{8}{3}\right)=\frac{82}{27}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{2}{9} & -\frac{10}{9} \\
+ \frac{2}{3} & -\frac{7}{9} \\
+ -\frac{8}{9} & -\frac{8}{9} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{13}{9} \\
+ -\frac{8}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \frac{266}{81} \\
+ \fbox{$\frac{82}{27}$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{2}{9} & -\frac{10}{9} \\
+ \frac{2}{3} & -\frac{7}{9} \\
+ -\frac{8}{9} & -\frac{8}{9} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{13}{9} \\
+ -\frac{8}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \frac{266}{81} \\
+ \frac{82}{27} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{8}{9}\right)\, \times \, \frac{13}{9}+\left(-\frac{8}{9}\right)\, \left(-\frac{8}{3}\right)=\frac{88}{81}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ \frac{2}{9} & -\frac{10}{9} \\
+ \frac{2}{3} & -\frac{7}{9} \\
+ -\frac{8}{9} & -\frac{8}{9} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{13}{9} \\
+ -\frac{8}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \frac{266}{81} \\
+ \frac{82}{27} \\
+ \fbox{$\frac{88}{81}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/1920.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/1920.txt
new file mode 100644
index 0000000000000000000000000000000000000000..34e19a565426558bd2188f69c91e26dfcf83849b
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/1920.txt
@@ -0,0 +1,390 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ 1 & 2 & -1 \\
+ -3 & -1 & 3 \\
+ 2 & 1 & 0 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 2 & 1 \\
+ 1 & -3 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ 1 & 2 & -1 \\
+ -3 & -1 & 3 \\
+ 2 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 2 & 1 \\
+ 1 & -3 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 2. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 2: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 1 & 2 & -1 \\
+ -3 & -1 & 3 \\
+ 2 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 2 & 1 \\
+ 1 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 1 & 2 & -1 \\
+ -3 & -1 & 3 \\
+ 2 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 2 & 1 \\
+ 1 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1\ 1+2\ 2+(-1)\, \times \, 1=4. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 1 & 2 & -1 \\
+ -3 & -1 & 3 \\
+ 2 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 2 & 1 \\
+ 1 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \fbox{$4$} & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 1 & 2 & -1 \\
+ -3 & -1 & 3 \\
+ 2 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 2 & 1 \\
+ 1 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1\ 2+2\ 1+(-1)\, (-3)=7. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 1 & 2 & -1 \\
+ -3 & -1 & 3 \\
+ 2 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 2 & 1 \\
+ 1 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & \fbox{$7$} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 1 & 2 & -1 \\
+ -3 & -1 & 3 \\
+ 2 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 2 & 1 \\
+ 1 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & 7 \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-3)\, \times \, 1+(-1)\, \times \, 2+3\ 1=-2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 1 & 2 & -1 \\
+ -3 & -1 & 3 \\
+ 2 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 2 & 1 \\
+ 1 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & 7 \\
+ \fbox{$-2$} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 1 & 2 & -1 \\
+ -3 & -1 & 3 \\
+ 2 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 2 & 1 \\
+ 1 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & 7 \\
+ -2 & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-3)\, \times \, 2+(-1)\, \times \, 1+3 (-3)=-16. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 1 & 2 & -1 \\
+ -3 & -1 & 3 \\
+ 2 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 2 & 1 \\
+ 1 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & 7 \\
+ -2 & \fbox{$-16$} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 1 & 2 & -1 \\
+ -3 & -1 & 3 \\
+ 2 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 2 & 1 \\
+ 1 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & 7 \\
+ -2 & -16 \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2\ 1+1\ 2+0\ 1=4. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 1 & 2 & -1 \\
+ -3 & -1 & 3 \\
+ 2 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 2 & 1 \\
+ 1 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & 7 \\
+ -2 & -16 \\
+ \fbox{$4$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 1 & 2 & -1 \\
+ -3 & -1 & 3 \\
+ 2 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 2 & 1 \\
+ 1 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & 7 \\
+ -2 & -16 \\
+ 4 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2\ 2+1\ 1+0 (-3)=5. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ 1 & 2 & -1 \\
+ -3 & -1 & 3 \\
+ 2 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 2 & 1 \\
+ 1 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & 7 \\
+ -2 & -16 \\
+ 4 & \fbox{$5$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/1989.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/1989.txt
new file mode 100644
index 0000000000000000000000000000000000000000..53de4e39a39e60c107baa2e99dbe0c2d829fbd0d
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/1989.txt
@@ -0,0 +1,159 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ -3 & 0 \\
+ 1 & 0 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -3 \\
+ 3 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ -3 & 0 \\
+ 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -3 \\
+ 3 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -3 & 0 \\
+ 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -3 \\
+ 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -3 & 0 \\
+ 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -3 \\
+ 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-3)\, (-3)+0\ 3=9. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -3 & 0 \\
+ 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -3 \\
+ 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$9$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -3 & 0 \\
+ 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -3 \\
+ 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 9 \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1 (-3)+0\ 3=-3. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ -3 & 0 \\
+ 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -3 \\
+ 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 9 \\
+ \fbox{$-3$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/2249.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/2249.txt
new file mode 100644
index 0000000000000000000000000000000000000000..50947cf6419b51265741c7b7e35cde7d5734eaaa
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/2249.txt
@@ -0,0 +1,166 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ -2 & -2 & 3 \\
+ 2 & 2 & -1 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -3 \\
+ 3 \\
+ 3 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & -2 & 3 \\
+ 2 & 2 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -3 \\
+ 3 \\
+ 3 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & -2 & 3 \\
+ 2 & 2 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -3 \\
+ 3 \\
+ 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & -2 & 3 \\
+ 2 & 2 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -3 \\
+ 3 \\
+ 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, (-3)+(-2)\, \times \, 3+3\ 3=9. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & -2 & 3 \\
+ 2 & 2 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -3 \\
+ 3 \\
+ 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$9$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & -2 & 3 \\
+ 2 & 2 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -3 \\
+ 3 \\
+ 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 9 \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2 (-3)+2\ 3+(-1)\, \times \, 3=-3. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ -2 & -2 & 3 \\
+ 2 & 2 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -3 \\
+ 3 \\
+ 3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 9 \\
+ \fbox{$-3$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/2282.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/2282.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6d29be77f66a5f276306a66b34c7d8651cbc52a4
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/2282.txt
@@ -0,0 +1,549 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ \frac{1}{3} & -1 & 0 \\
+ \frac{2}{3} & -\frac{2}{3} & -2 \\
+ \frac{4}{3} & -\frac{2}{3} & \frac{8}{3} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ \frac{8}{3} & 1 & -\frac{7}{3} \\
+ \frac{8}{3} & 3 & 0 \\
+ -\frac{1}{3} & -\frac{8}{3} & \frac{7}{3} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{1}{3} & -1 & 0 \\
+ \frac{2}{3} & -\frac{2}{3} & -2 \\
+ \frac{4}{3} & -\frac{2}{3} & \frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{8}{3} & 1 & -\frac{7}{3} \\
+ \frac{8}{3} & 3 & 0 \\
+ -\frac{1}{3} & -\frac{8}{3} & \frac{7}{3} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{1}{3} & -1 & 0 \\
+ \frac{2}{3} & -\frac{2}{3} & -2 \\
+ \frac{4}{3} & -\frac{2}{3} & \frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{8}{3} & 1 & -\frac{7}{3} \\
+ \frac{8}{3} & 3 & 0 \\
+ -\frac{1}{3} & -\frac{8}{3} & \frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{1}{3} & -1 & 0 \\
+ \frac{2}{3} & -\frac{2}{3} & -2 \\
+ \frac{4}{3} & -\frac{2}{3} & \frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{8}{3} & 1 & -\frac{7}{3} \\
+ \frac{8}{3} & 3 & 0 \\
+ -\frac{1}{3} & -\frac{8}{3} & \frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{8}{3\ 3}+(-1)\, \times \, \frac{8}{3}+\frac{1}{3} (-0)=-\frac{16}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{1}{3} & -1 & 0 \\
+ \frac{2}{3} & -\frac{2}{3} & -2 \\
+ \frac{4}{3} & -\frac{2}{3} & \frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{8}{3} & 1 & -\frac{7}{3} \\
+ \frac{8}{3} & 3 & 0 \\
+ -\frac{1}{3} & -\frac{8}{3} & \frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$-\frac{16}{9}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{1}{3} & -1 & 0 \\
+ \frac{2}{3} & -\frac{2}{3} & -2 \\
+ \frac{4}{3} & -\frac{2}{3} & \frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{8}{3} & 1 & -\frac{7}{3} \\
+ \frac{8}{3} & 3 & 0 \\
+ -\frac{1}{3} & -\frac{8}{3} & \frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{16}{9} & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{3}+(-1)\, \times \, 3+\frac{0 (-8)}{3}=-\frac{8}{3}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{1}{3} & -1 & 0 \\
+ \frac{2}{3} & -\frac{2}{3} & -2 \\
+ \frac{4}{3} & -\frac{2}{3} & \frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{8}{3} & 1 & -\frac{7}{3} \\
+ \frac{8}{3} & 3 & 0 \\
+ -\frac{1}{3} & -\frac{8}{3} & \frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{16}{9} & \fbox{$-\frac{8}{3}$} & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{1}{3} & -1 & 0 \\
+ \frac{2}{3} & -\frac{2}{3} & -2 \\
+ \frac{4}{3} & -\frac{2}{3} & \frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{8}{3} & 1 & -\frac{7}{3} \\
+ \frac{8}{3} & 3 & 0 \\
+ -\frac{1}{3} & -\frac{8}{3} & \frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{16}{9} & -\frac{8}{3} & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }-\frac{7}{3\ 3}+(-1)\, \times \, 0+\frac{0\ 7}{3}=-\frac{7}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{1}{3} & -1 & 0 \\
+ \frac{2}{3} & -\frac{2}{3} & -2 \\
+ \frac{4}{3} & -\frac{2}{3} & \frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{8}{3} & 1 & -\frac{7}{3} \\
+ \frac{8}{3} & 3 & 0 \\
+ -\frac{1}{3} & -\frac{8}{3} & \frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{16}{9} & -\frac{8}{3} & \fbox{$-\frac{7}{9}$} \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{1}{3} & -1 & 0 \\
+ \frac{2}{3} & -\frac{2}{3} & -2 \\
+ \frac{4}{3} & -\frac{2}{3} & \frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{8}{3} & 1 & -\frac{7}{3} \\
+ \frac{8}{3} & 3 & 0 \\
+ -\frac{1}{3} & -\frac{8}{3} & \frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{16}{9} & -\frac{8}{3} & -\frac{7}{9} \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2\ 8}{3\ 3}+\left(-\frac{2}{3}\right)\, \times \, \frac{8}{3}+\frac{2}{3}=\frac{2}{3}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{1}{3} & -1 & 0 \\
+ \frac{2}{3} & -\frac{2}{3} & -2 \\
+ \frac{4}{3} & -\frac{2}{3} & \frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{8}{3} & 1 & -\frac{7}{3} \\
+ \frac{8}{3} & 3 & 0 \\
+ -\frac{1}{3} & -\frac{8}{3} & \frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{16}{9} & -\frac{8}{3} & -\frac{7}{9} \\
+ \fbox{$\frac{2}{3}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{1}{3} & -1 & 0 \\
+ \frac{2}{3} & -\frac{2}{3} & -2 \\
+ \frac{4}{3} & -\frac{2}{3} & \frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{8}{3} & 1 & -\frac{7}{3} \\
+ \frac{8}{3} & 3 & 0 \\
+ -\frac{1}{3} & -\frac{8}{3} & \frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{16}{9} & -\frac{8}{3} & -\frac{7}{9} \\
+ \frac{2}{3} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2}{3}+\left(-\frac{2}{3}\right)\, \times \, 3+(-2)\, \left(-\frac{8}{3}\right)=4. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{1}{3} & -1 & 0 \\
+ \frac{2}{3} & -\frac{2}{3} & -2 \\
+ \frac{4}{3} & -\frac{2}{3} & \frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{8}{3} & 1 & -\frac{7}{3} \\
+ \frac{8}{3} & 3 & 0 \\
+ -\frac{1}{3} & -\frac{8}{3} & \frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{16}{9} & -\frac{8}{3} & -\frac{7}{9} \\
+ \frac{2}{3} & \fbox{$4$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{1}{3} & -1 & 0 \\
+ \frac{2}{3} & -\frac{2}{3} & -2 \\
+ \frac{4}{3} & -\frac{2}{3} & \frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{8}{3} & 1 & -\frac{7}{3} \\
+ \frac{8}{3} & 3 & 0 \\
+ -\frac{1}{3} & -\frac{8}{3} & \frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{16}{9} & -\frac{8}{3} & -\frac{7}{9} \\
+ \frac{2}{3} & 4 & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2 (-7)}{3\ 3}+\left(-\frac{2}{3}\right)\, \times \, 0+(-2)\, \times \, \frac{7}{3}=-\frac{56}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{1}{3} & -1 & 0 \\
+ \frac{2}{3} & -\frac{2}{3} & -2 \\
+ \frac{4}{3} & -\frac{2}{3} & \frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{8}{3} & 1 & -\frac{7}{3} \\
+ \frac{8}{3} & 3 & 0 \\
+ -\frac{1}{3} & -\frac{8}{3} & \frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{16}{9} & -\frac{8}{3} & -\frac{7}{9} \\
+ \frac{2}{3} & 4 & \fbox{$-\frac{56}{9}$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{1}{3} & -1 & 0 \\
+ \frac{2}{3} & -\frac{2}{3} & -2 \\
+ \frac{4}{3} & -\frac{2}{3} & \frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{8}{3} & 1 & -\frac{7}{3} \\
+ \frac{8}{3} & 3 & 0 \\
+ -\frac{1}{3} & -\frac{8}{3} & \frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{16}{9} & -\frac{8}{3} & -\frac{7}{9} \\
+ \frac{2}{3} & 4 & -\frac{56}{9} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{4\ 8}{3\ 3}+\left(-\frac{2}{3}\right)\, \times \, \frac{8}{3}+\frac{1}{3} \left(-\frac{8}{3}\right)=\frac{8}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{1}{3} & -1 & 0 \\
+ \frac{2}{3} & -\frac{2}{3} & -2 \\
+ \frac{4}{3} & -\frac{2}{3} & \frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{8}{3} & 1 & -\frac{7}{3} \\
+ \frac{8}{3} & 3 & 0 \\
+ -\frac{1}{3} & -\frac{8}{3} & \frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{16}{9} & -\frac{8}{3} & -\frac{7}{9} \\
+ \frac{2}{3} & 4 & -\frac{56}{9} \\
+ \fbox{$\frac{8}{9}$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{1}{3} & -1 & 0 \\
+ \frac{2}{3} & -\frac{2}{3} & -2 \\
+ \frac{4}{3} & -\frac{2}{3} & \frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{8}{3} & 1 & -\frac{7}{3} \\
+ \frac{8}{3} & 3 & 0 \\
+ -\frac{1}{3} & -\frac{8}{3} & \frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{16}{9} & -\frac{8}{3} & -\frac{7}{9} \\
+ \frac{2}{3} & 4 & -\frac{56}{9} \\
+ \frac{8}{9} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{4}{3}+\left(-\frac{2}{3}\right)\, \times \, 3+\frac{8 (-8)}{3\ 3}=-\frac{70}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{1}{3} & -1 & 0 \\
+ \frac{2}{3} & -\frac{2}{3} & -2 \\
+ \frac{4}{3} & -\frac{2}{3} & \frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{8}{3} & 1 & -\frac{7}{3} \\
+ \frac{8}{3} & 3 & 0 \\
+ -\frac{1}{3} & -\frac{8}{3} & \frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{16}{9} & -\frac{8}{3} & -\frac{7}{9} \\
+ \frac{2}{3} & 4 & -\frac{56}{9} \\
+ \frac{8}{9} & \fbox{$-\frac{70}{9}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{1}{3} & -1 & 0 \\
+ \frac{2}{3} & -\frac{2}{3} & -2 \\
+ \frac{4}{3} & -\frac{2}{3} & \frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{8}{3} & 1 & -\frac{7}{3} \\
+ \frac{8}{3} & 3 & 0 \\
+ -\frac{1}{3} & -\frac{8}{3} & \frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{16}{9} & -\frac{8}{3} & -\frac{7}{9} \\
+ \frac{2}{3} & 4 & -\frac{56}{9} \\
+ \frac{8}{9} & -\frac{70}{9} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{4 (-7)}{3\ 3}+\left(-\frac{2}{3}\right)\, \times \, 0+\frac{8\ 7}{3\ 3}=\frac{28}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ \frac{1}{3} & -1 & 0 \\
+ \frac{2}{3} & -\frac{2}{3} & -2 \\
+ \frac{4}{3} & -\frac{2}{3} & \frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{8}{3} & 1 & -\frac{7}{3} \\
+ \frac{8}{3} & 3 & 0 \\
+ -\frac{1}{3} & -\frac{8}{3} & \frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{16}{9} & -\frac{8}{3} & -\frac{7}{9} \\
+ \frac{2}{3} & 4 & -\frac{56}{9} \\
+ \frac{8}{9} & -\frac{70}{9} & \fbox{$\frac{28}{9}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/238.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/238.txt
new file mode 100644
index 0000000000000000000000000000000000000000..11ccd5724a8c9074174b49d725cc2a100771c1f3
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/238.txt
@@ -0,0 +1,222 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ 2 & -1 \\
+ -2 & -2 \\
+ 3 & 0 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -1 \\
+ -3 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ 2 & -1 \\
+ -2 & -2 \\
+ 3 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -1 \\
+ -3 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & -1 \\
+ -2 & -2 \\
+ 3 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -1 \\
+ -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & -1 \\
+ -2 & -2 \\
+ 3 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -1 \\
+ -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2 (-1)+(-1)\, (-3)=1. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & -1 \\
+ -2 & -2 \\
+ 3 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -1 \\
+ -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$1$} \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & -1 \\
+ -2 & -2 \\
+ 3 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -1 \\
+ -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 1 \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, (-1)+(-2)\, (-3)=8. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & -1 \\
+ -2 & -2 \\
+ 3 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -1 \\
+ -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 1 \\
+ \fbox{$8$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & -1 \\
+ -2 & -2 \\
+ 3 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -1 \\
+ -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 1 \\
+ 8 \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }3 (-1)+0 (-3)=-3. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ 2 & -1 \\
+ -2 & -2 \\
+ 3 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -1 \\
+ -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 1 \\
+ 8 \\
+ \fbox{$-3$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/2581.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/2581.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ae3cf9a11d5d1c72ee69c480e97ad0ad4203dde0
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/2581.txt
@@ -0,0 +1,159 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ 1 & -\frac{13}{7} \\
+ \frac{20}{7} & -\frac{13}{7} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 3 \\
+ \frac{11}{7} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ 1 & -\frac{13}{7} \\
+ \frac{20}{7} & -\frac{13}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 3 \\
+ \frac{11}{7} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 1 & -\frac{13}{7} \\
+ \frac{20}{7} & -\frac{13}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 3 \\
+ \frac{11}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 1 & -\frac{13}{7} \\
+ \frac{20}{7} & -\frac{13}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 3 \\
+ \frac{11}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1\ 3+\left(-\frac{13}{7}\right)\, \times \, \frac{11}{7}=\frac{4}{49}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 1 & -\frac{13}{7} \\
+ \frac{20}{7} & -\frac{13}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 3 \\
+ \frac{11}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$\frac{4}{49}$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 1 & -\frac{13}{7} \\
+ \frac{20}{7} & -\frac{13}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 3 \\
+ \frac{11}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \frac{4}{49} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{20\ 3}{7}+\left(-\frac{13}{7}\right)\, \times \, \frac{11}{7}=\frac{277}{49}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ 1 & -\frac{13}{7} \\
+ \frac{20}{7} & -\frac{13}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 3 \\
+ \frac{11}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \frac{4}{49} \\
+ \fbox{$\frac{277}{49}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/2642.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/2642.txt
new file mode 100644
index 0000000000000000000000000000000000000000..106b75167ef47aeb563bbed01357983938470611
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/2642.txt
@@ -0,0 +1,159 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ -2 & -2 \\
+ -2 & -2 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 0 \\
+ -1 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ -2 & -2 \\
+ -2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 0 \\
+ -1 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -2 & -2 \\
+ -2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 0 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -2 & -2 \\
+ -2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 0 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, \times \, 0+(-2)\, (-1)=2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -2 & -2 \\
+ -2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 0 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$2$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -2 & -2 \\
+ -2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 0 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 2 \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, \times \, 0+(-2)\, (-1)=2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ -2 & -2 \\
+ -2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 0 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 2 \\
+ \fbox{$2$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/2649.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/2649.txt
new file mode 100644
index 0000000000000000000000000000000000000000..32f70bea25154449917a16f95a5cdff794eb85fc
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/2649.txt
@@ -0,0 +1,390 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ \frac{5}{7} & 1 & \frac{15}{7} \\
+ \frac{16}{7} & -\frac{5}{7} & -\frac{6}{7} \\
+ \frac{20}{7} & -\frac{5}{7} & -\frac{1}{7} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{cc}
+ -\frac{4}{7} & \frac{5}{7} \\
+ \frac{2}{7} & \frac{8}{7} \\
+ 2 & -\frac{2}{7} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{7} & 1 & \frac{15}{7} \\
+ \frac{16}{7} & -\frac{5}{7} & -\frac{6}{7} \\
+ \frac{20}{7} & -\frac{5}{7} & -\frac{1}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{4}{7} & \frac{5}{7} \\
+ \frac{2}{7} & \frac{8}{7} \\
+ 2 & -\frac{2}{7} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 2. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 2: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{7} & 1 & \frac{15}{7} \\
+ \frac{16}{7} & -\frac{5}{7} & -\frac{6}{7} \\
+ \frac{20}{7} & -\frac{5}{7} & -\frac{1}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{4}{7} & \frac{5}{7} \\
+ \frac{2}{7} & \frac{8}{7} \\
+ 2 & -\frac{2}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{7} & 1 & \frac{15}{7} \\
+ \frac{16}{7} & -\frac{5}{7} & -\frac{6}{7} \\
+ \frac{20}{7} & -\frac{5}{7} & -\frac{1}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{4}{7} & \frac{5}{7} \\
+ \frac{2}{7} & \frac{8}{7} \\
+ 2 & -\frac{2}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{5 (-4)}{7\ 7}+\frac{2}{7}+\frac{15\ 2}{7}=\frac{204}{49}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{7} & 1 & \frac{15}{7} \\
+ \frac{16}{7} & -\frac{5}{7} & -\frac{6}{7} \\
+ \frac{20}{7} & -\frac{5}{7} & -\frac{1}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{4}{7} & \frac{5}{7} \\
+ \frac{2}{7} & \frac{8}{7} \\
+ 2 & -\frac{2}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \fbox{$\frac{204}{49}$} & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{7} & 1 & \frac{15}{7} \\
+ \frac{16}{7} & -\frac{5}{7} & -\frac{6}{7} \\
+ \frac{20}{7} & -\frac{5}{7} & -\frac{1}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{4}{7} & \frac{5}{7} \\
+ \frac{2}{7} & \frac{8}{7} \\
+ 2 & -\frac{2}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{204}{49} & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{5\ 5}{7\ 7}+\frac{8}{7}+\frac{15 (-2)}{7\ 7}=\frac{51}{49}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{7} & 1 & \frac{15}{7} \\
+ \frac{16}{7} & -\frac{5}{7} & -\frac{6}{7} \\
+ \frac{20}{7} & -\frac{5}{7} & -\frac{1}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{4}{7} & \frac{5}{7} \\
+ \frac{2}{7} & \frac{8}{7} \\
+ 2 & -\frac{2}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{204}{49} & \fbox{$\frac{51}{49}$} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{7} & 1 & \frac{15}{7} \\
+ \frac{16}{7} & -\frac{5}{7} & -\frac{6}{7} \\
+ \frac{20}{7} & -\frac{5}{7} & -\frac{1}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{4}{7} & \frac{5}{7} \\
+ \frac{2}{7} & \frac{8}{7} \\
+ 2 & -\frac{2}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{204}{49} & \frac{51}{49} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{16 (-4)}{7\ 7}+\left(-\frac{5}{7}\right)\, \times \, \frac{2}{7}+\left(-\frac{6}{7}\right)\, \times \, 2=-\frac{158}{49}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{7} & 1 & \frac{15}{7} \\
+ \frac{16}{7} & -\frac{5}{7} & -\frac{6}{7} \\
+ \frac{20}{7} & -\frac{5}{7} & -\frac{1}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{4}{7} & \frac{5}{7} \\
+ \frac{2}{7} & \frac{8}{7} \\
+ 2 & -\frac{2}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{204}{49} & \frac{51}{49} \\
+ \fbox{$-\frac{158}{49}$} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{7} & 1 & \frac{15}{7} \\
+ \frac{16}{7} & -\frac{5}{7} & -\frac{6}{7} \\
+ \frac{20}{7} & -\frac{5}{7} & -\frac{1}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{4}{7} & \frac{5}{7} \\
+ \frac{2}{7} & \frac{8}{7} \\
+ 2 & -\frac{2}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{204}{49} & \frac{51}{49} \\
+ -\frac{158}{49} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{16\ 5}{7\ 7}+\left(-\frac{5}{7}\right)\, \times \, \frac{8}{7}+\left(-\frac{6}{7}\right)\, \left(-\frac{2}{7}\right)=\frac{52}{49}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{7} & 1 & \frac{15}{7} \\
+ \frac{16}{7} & -\frac{5}{7} & -\frac{6}{7} \\
+ \frac{20}{7} & -\frac{5}{7} & -\frac{1}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{4}{7} & \frac{5}{7} \\
+ \frac{2}{7} & \frac{8}{7} \\
+ 2 & -\frac{2}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{204}{49} & \frac{51}{49} \\
+ -\frac{158}{49} & \fbox{$\frac{52}{49}$} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{7} & 1 & \frac{15}{7} \\
+ \frac{16}{7} & -\frac{5}{7} & -\frac{6}{7} \\
+ \frac{20}{7} & -\frac{5}{7} & -\frac{1}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{4}{7} & \frac{5}{7} \\
+ \frac{2}{7} & \frac{8}{7} \\
+ 2 & -\frac{2}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{204}{49} & \frac{51}{49} \\
+ -\frac{158}{49} & \frac{52}{49} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{20 (-4)}{7\ 7}+\left(-\frac{5}{7}\right)\, \times \, \frac{2}{7}+\frac{1}{7} (-2)=-\frac{104}{49}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{7} & 1 & \frac{15}{7} \\
+ \frac{16}{7} & -\frac{5}{7} & -\frac{6}{7} \\
+ \frac{20}{7} & -\frac{5}{7} & -\frac{1}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{4}{7} & \frac{5}{7} \\
+ \frac{2}{7} & \frac{8}{7} \\
+ 2 & -\frac{2}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{204}{49} & \frac{51}{49} \\
+ -\frac{158}{49} & \frac{52}{49} \\
+ \fbox{$-\frac{104}{49}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{7} & 1 & \frac{15}{7} \\
+ \frac{16}{7} & -\frac{5}{7} & -\frac{6}{7} \\
+ \frac{20}{7} & -\frac{5}{7} & -\frac{1}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{4}{7} & \frac{5}{7} \\
+ \frac{2}{7} & \frac{8}{7} \\
+ 2 & -\frac{2}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{204}{49} & \frac{51}{49} \\
+ -\frac{158}{49} & \frac{52}{49} \\
+ -\frac{104}{49} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{20\ 5}{7\ 7}+\left(-\frac{5}{7}\right)\, \times \, \frac{8}{7}+\frac{2}{7\ 7}=\frac{62}{49}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ \frac{5}{7} & 1 & \frac{15}{7} \\
+ \frac{16}{7} & -\frac{5}{7} & -\frac{6}{7} \\
+ \frac{20}{7} & -\frac{5}{7} & -\frac{1}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{4}{7} & \frac{5}{7} \\
+ \frac{2}{7} & \frac{8}{7} \\
+ 2 & -\frac{2}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{204}{49} & \frac{51}{49} \\
+ -\frac{158}{49} & \frac{52}{49} \\
+ -\frac{104}{49} & \fbox{$\frac{62}{49}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/2671.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/2671.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7d1fe86157cfdcbd87a3af30dcfc78e57748e78b
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/2671.txt
@@ -0,0 +1,347 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ -3 & 0 \\
+ 2 & 0 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ 0 & 0 & -2 \\
+ 2 & -2 & -3 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ -3 & 0 \\
+ 2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & 0 & -2 \\
+ 2 & -2 & -3 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -3 & 0 \\
+ 2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & 0 & -2 \\
+ 2 & -2 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -3 & 0 \\
+ 2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & 0 & -2 \\
+ 2 & -2 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-3)\, \times \, 0+0\ 2=0. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -3 & 0 \\
+ 2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & 0 & -2 \\
+ 2 & -2 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$0$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -3 & 0 \\
+ 2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & 0 & -2 \\
+ 2 & -2 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-3)\, \times \, 0+0 (-2)=0. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -3 & 0 \\
+ 2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & 0 & -2 \\
+ 2 & -2 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & \fbox{$0$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -3 & 0 \\
+ 2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & 0 & -2 \\
+ 2 & -2 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & 0 & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-3)\, (-2)+0 (-3)=6. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -3 & 0 \\
+ 2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & 0 & -2 \\
+ 2 & -2 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & 0 & \fbox{$6$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -3 & 0 \\
+ 2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & 0 & -2 \\
+ 2 & -2 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & 0 & 6 \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2\ 0+0\ 2=0. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -3 & 0 \\
+ 2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & 0 & -2 \\
+ 2 & -2 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & 0 & 6 \\
+ \fbox{$0$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -3 & 0 \\
+ 2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & 0 & -2 \\
+ 2 & -2 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & 0 & 6 \\
+ 0 & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2\ 0+0 (-2)=0. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -3 & 0 \\
+ 2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & 0 & -2 \\
+ 2 & -2 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & 0 & 6 \\
+ 0 & \fbox{$0$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -3 & 0 \\
+ 2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & 0 & -2 \\
+ 2 & -2 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & 0 & 6 \\
+ 0 & 0 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2 (-2)+0 (-3)=-4. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ -3 & 0 \\
+ 2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & 0 & -2 \\
+ 2 & -2 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & 0 & 6 \\
+ 0 & 0 & \fbox{$-4$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/2742.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/2742.txt
new file mode 100644
index 0000000000000000000000000000000000000000..33a4b0e1e8c690e5f843785c69e128114b6f6a07
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/2742.txt
@@ -0,0 +1,159 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ 0 & 0 \\
+ -2 & 1 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -2 \\
+ -3 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ 0 & 0 \\
+ -2 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -2 \\
+ -3 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 0 & 0 \\
+ -2 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -2 \\
+ -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 0 & 0 \\
+ -2 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -2 \\
+ -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0 (-2)+0 (-3)=0. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 0 & 0 \\
+ -2 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -2 \\
+ -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$0$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 0 & 0 \\
+ -2 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -2 \\
+ -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 0 \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, (-2)+1 (-3)=1. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ 0 & 0 \\
+ -2 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -2 \\
+ -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 0 \\
+ \fbox{$1$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/2757.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/2757.txt
new file mode 100644
index 0000000000000000000000000000000000000000..93360daa154e0116b166cf6b7aecd1ddc6f3d105
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/2757.txt
@@ -0,0 +1,347 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ 3 & 2 \\
+ -2 & 0 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ -1 & -3 & 1 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ 3 & 2 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -3 & 1 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 3 & 2 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -3 & 1 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 3 & 2 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -3 & 1 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }3 (-1)+2 (-1)=-5. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 3 & 2 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -3 & 1 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$-5$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 3 & 2 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -3 & 1 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }3 (-3)+2\ 1=-7. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 3 & 2 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -3 & 1 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & \fbox{$-7$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 3 & 2 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -3 & 1 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -7 & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }3\ 1+2\ 2=7. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 3 & 2 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -3 & 1 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -7 & \fbox{$7$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 3 & 2 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -3 & 1 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -7 & 7 \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, (-1)+0 (-1)=2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 3 & 2 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -3 & 1 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -7 & 7 \\
+ \fbox{$2$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 3 & 2 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -3 & 1 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -7 & 7 \\
+ 2 & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, (-3)+0\ 1=6. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 3 & 2 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -3 & 1 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -7 & 7 \\
+ 2 & \fbox{$6$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 3 & 2 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -3 & 1 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -7 & 7 \\
+ 2 & 6 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, \times \, 1+0\ 2=-2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ 3 & 2 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -3 & 1 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -7 & 7 \\
+ 2 & 6 & \fbox{$-2$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/2774.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/2774.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c8b4fd359ab2d6956bfb7cba08ee04c23b29ab2d
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/2774.txt
@@ -0,0 +1,222 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ 1 & -2 \\
+ 0 & 0 \\
+ -2 & 0 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 3 \\
+ -2 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ 1 & -2 \\
+ 0 & 0 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 3 \\
+ -2 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 1 & -2 \\
+ 0 & 0 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 3 \\
+ -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 1 & -2 \\
+ 0 & 0 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 3 \\
+ -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1\ 3+(-2)\, (-2)=7. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 1 & -2 \\
+ 0 & 0 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 3 \\
+ -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$7$} \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 1 & -2 \\
+ 0 & 0 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 3 \\
+ -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 7 \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0\ 3+0 (-2)=0. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 1 & -2 \\
+ 0 & 0 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 3 \\
+ -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 7 \\
+ \fbox{$0$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 1 & -2 \\
+ 0 & 0 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 3 \\
+ -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 7 \\
+ 0 \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, \times \, 3+0 (-2)=-6. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ 1 & -2 \\
+ 0 & 0 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 3 \\
+ -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 7 \\
+ 0 \\
+ \fbox{$-6$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/2779.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/2779.txt
new file mode 100644
index 0000000000000000000000000000000000000000..48438e51d0aed13eb2ff2ccd8ccb7c35714186d0
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/2779.txt
@@ -0,0 +1,166 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ -\frac{2}{7} & -\frac{4}{7} & \frac{17}{7} \\
+ \frac{4}{7} & \frac{8}{7} & \frac{19}{7} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 2 \\
+ 1 \\
+ -\frac{8}{7} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{2}{7} & -\frac{4}{7} & \frac{17}{7} \\
+ \frac{4}{7} & \frac{8}{7} & \frac{19}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 2 \\
+ 1 \\
+ -\frac{8}{7} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{2}{7} & -\frac{4}{7} & \frac{17}{7} \\
+ \frac{4}{7} & \frac{8}{7} & \frac{19}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 2 \\
+ 1 \\
+ -\frac{8}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{2}{7} & -\frac{4}{7} & \frac{17}{7} \\
+ \frac{4}{7} & \frac{8}{7} & \frac{19}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 2 \\
+ 1 \\
+ -\frac{8}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{2}{7}\right)\, \times \, 2+\left(-\frac{4}{7}\right)\, \times \, 1+\frac{17 (-8)}{7\ 7}=-\frac{192}{49}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{2}{7} & -\frac{4}{7} & \frac{17}{7} \\
+ \frac{4}{7} & \frac{8}{7} & \frac{19}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 2 \\
+ 1 \\
+ -\frac{8}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$-\frac{192}{49}$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{2}{7} & -\frac{4}{7} & \frac{17}{7} \\
+ \frac{4}{7} & \frac{8}{7} & \frac{19}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 2 \\
+ 1 \\
+ -\frac{8}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ -\frac{192}{49} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{4\ 2}{7}+\frac{8}{7}+\frac{19 (-8)}{7\ 7}=-\frac{40}{49}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ -\frac{2}{7} & -\frac{4}{7} & \frac{17}{7} \\
+ \frac{4}{7} & \frac{8}{7} & \frac{19}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 2 \\
+ 1 \\
+ -\frac{8}{7} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ -\frac{192}{49} \\
+ \fbox{$-\frac{40}{49}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/2807.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/2807.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b9d63afca5f77ba2a6f81a9ba6346ab4afe446e6
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/2807.txt
@@ -0,0 +1,347 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ 2 & \frac{1}{4} \\
+ -\frac{1}{4} & 3 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ 2 & \frac{11}{4} & -2 \\
+ -\frac{7}{4} & 1 & \frac{1}{2} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{1}{4} \\
+ -\frac{1}{4} & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 2 & \frac{11}{4} & -2 \\
+ -\frac{7}{4} & 1 & \frac{1}{2} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{1}{4} \\
+ -\frac{1}{4} & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 2 & \frac{11}{4} & -2 \\
+ -\frac{7}{4} & 1 & \frac{1}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{1}{4} \\
+ -\frac{1}{4} & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 2 & \frac{11}{4} & -2 \\
+ -\frac{7}{4} & 1 & \frac{1}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2\ 2-\frac{7}{4\ 4}=\frac{57}{16}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{1}{4} \\
+ -\frac{1}{4} & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 2 & \frac{11}{4} & -2 \\
+ -\frac{7}{4} & 1 & \frac{1}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$\frac{57}{16}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{1}{4} \\
+ -\frac{1}{4} & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 2 & \frac{11}{4} & -2 \\
+ -\frac{7}{4} & 1 & \frac{1}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{57}{16} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2\ 11}{4}+\frac{1}{4}=\frac{23}{4}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{1}{4} \\
+ -\frac{1}{4} & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 2 & \frac{11}{4} & -2 \\
+ -\frac{7}{4} & 1 & \frac{1}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{57}{16} & \fbox{$\frac{23}{4}$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{1}{4} \\
+ -\frac{1}{4} & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 2 & \frac{11}{4} & -2 \\
+ -\frac{7}{4} & 1 & \frac{1}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{57}{16} & \frac{23}{4} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2 (-2)+\frac{1}{4\ 2}=-\frac{31}{8}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{1}{4} \\
+ -\frac{1}{4} & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 2 & \frac{11}{4} & -2 \\
+ -\frac{7}{4} & 1 & \frac{1}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{57}{16} & \frac{23}{4} & \fbox{$-\frac{31}{8}$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{1}{4} \\
+ -\frac{1}{4} & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 2 & \frac{11}{4} & -2 \\
+ -\frac{7}{4} & 1 & \frac{1}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{57}{16} & \frac{23}{4} & -\frac{31}{8} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{4} (-2)+\frac{3 (-7)}{4}=-\frac{23}{4}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{1}{4} \\
+ -\frac{1}{4} & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 2 & \frac{11}{4} & -2 \\
+ -\frac{7}{4} & 1 & \frac{1}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{57}{16} & \frac{23}{4} & -\frac{31}{8} \\
+ \fbox{$-\frac{23}{4}$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{1}{4} \\
+ -\frac{1}{4} & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 2 & \frac{11}{4} & -2 \\
+ -\frac{7}{4} & 1 & \frac{1}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{57}{16} & \frac{23}{4} & -\frac{31}{8} \\
+ -\frac{23}{4} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{4} \left(-\frac{11}{4}\right)+3\ 1=\frac{37}{16}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{1}{4} \\
+ -\frac{1}{4} & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 2 & \frac{11}{4} & -2 \\
+ -\frac{7}{4} & 1 & \frac{1}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{57}{16} & \frac{23}{4} & -\frac{31}{8} \\
+ -\frac{23}{4} & \fbox{$\frac{37}{16}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{1}{4} \\
+ -\frac{1}{4} & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 2 & \frac{11}{4} & -2 \\
+ -\frac{7}{4} & 1 & \frac{1}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{57}{16} & \frac{23}{4} & -\frac{31}{8} \\
+ -\frac{23}{4} & \frac{37}{16} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2}{4}+\frac{3}{2}=2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ 2 & \frac{1}{4} \\
+ -\frac{1}{4} & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 2 & \frac{11}{4} & -2 \\
+ -\frac{7}{4} & 1 & \frac{1}{2} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{57}{16} & \frac{23}{4} & -\frac{31}{8} \\
+ -\frac{23}{4} & \frac{37}{16} & \fbox{$2$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/2883.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/2883.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0906b245d73f46373bb0a6f83bfae4f4e5ef5ca8
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/2883.txt
@@ -0,0 +1,159 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ 0 & 1 \\
+ -2 & 0 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 0 \\
+ 2 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ 0 & 1 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 0 \\
+ 2 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 0 & 1 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 0 \\
+ 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 0 & 1 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 0 \\
+ 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0\ 0+1\ 2=2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 0 & 1 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 0 \\
+ 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$2$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 0 & 1 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 0 \\
+ 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 2 \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, \times \, 0+0\ 2=0. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ 0 & 1 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 0 \\
+ 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 2 \\
+ \fbox{$0$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/291.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/291.txt
new file mode 100644
index 0000000000000000000000000000000000000000..09e5a8a5e296030db2221fff4917ebca7a3fc017
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/291.txt
@@ -0,0 +1,253 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ 2 & 0 \\
+ -1 & -1 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{cc}
+ 0 & -1 \\
+ -1 & 0 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ 2 & 0 \\
+ -1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & -1 \\
+ -1 & 0 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 2. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 2: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & 0 \\
+ -1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & -1 \\
+ -1 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & 0 \\
+ -1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & -1 \\
+ -1 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2\ 0+0 (-1)=0. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & 0 \\
+ -1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & -1 \\
+ -1 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \fbox{$0$} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & 0 \\
+ -1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & -1 \\
+ -1 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 0 & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2 (-1)+0\ 0=-2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & 0 \\
+ -1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & -1 \\
+ -1 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 0 & \fbox{$-2$} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & 0 \\
+ -1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & -1 \\
+ -1 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 0 & -2 \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, \times \, 0+(-1)\, (-1)=1. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & 0 \\
+ -1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & -1 \\
+ -1 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 0 & -2 \\
+ \fbox{$1$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & 0 \\
+ -1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & -1 \\
+ -1 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 0 & -2 \\
+ 1 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, (-1)+(-1)\, \times \, 0=1. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ 2 & 0 \\
+ -1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & -1 \\
+ -1 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 0 & -2 \\
+ 1 & \fbox{$1$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/298.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/298.txt
new file mode 100644
index 0000000000000000000000000000000000000000..370bad40742a0b6e2ff519a467a317d31082bae3
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/298.txt
@@ -0,0 +1,253 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 1 & -2 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{cc}
+ -2 & -2 \\
+ 3 & -3 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -2 & -2 \\
+ 3 & -3 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 2. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 2: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -2 & -2 \\
+ 3 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -2 & -2 \\
+ 3 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1 (-2)+2\ 3=4. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -2 & -2 \\
+ 3 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \fbox{$4$} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -2 & -2 \\
+ 3 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1 (-2)+2 (-3)=-8. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -2 & -2 \\
+ 3 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & \fbox{$-8$} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -2 & -2 \\
+ 3 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & -8 \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1 (-2)+(-2)\, \times \, 3=-8. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -2 & -2 \\
+ 3 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & -8 \\
+ \fbox{$-8$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -2 & -2 \\
+ 3 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & -8 \\
+ -8 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1 (-2)+(-2)\, (-3)=4. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ 1 & 2 \\
+ 1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -2 & -2 \\
+ 3 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & -8 \\
+ -8 & \fbox{$4$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/2984.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/2984.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4a121bdde6b8f4712fdc9a92b0f8deccc0bd6532
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/2984.txt
@@ -0,0 +1,390 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ -2 & 1 & -3 \\
+ 0 & 3 & 2 \\
+ -1 & 1 & -1 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{cc}
+ 3 & -3 \\
+ -1 & -1 \\
+ -2 & 0 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 1 & -3 \\
+ 0 & 3 & 2 \\
+ -1 & 1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 3 & -3 \\
+ -1 & -1 \\
+ -2 & 0 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 2. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 2: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & 1 & -3 \\
+ 0 & 3 & 2 \\
+ -1 & 1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 3 & -3 \\
+ -1 & -1 \\
+ -2 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 1 & -3 \\
+ 0 & 3 & 2 \\
+ -1 & 1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 3 & -3 \\
+ -1 & -1 \\
+ -2 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, \times \, 3+1 (-1)+(-3)\, (-2)=-1. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & 1 & -3 \\
+ 0 & 3 & 2 \\
+ -1 & 1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 3 & -3 \\
+ -1 & -1 \\
+ -2 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \fbox{$-1$} & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 1 & -3 \\
+ 0 & 3 & 2 \\
+ -1 & 1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 3 & -3 \\
+ -1 & -1 \\
+ -2 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -1 & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, (-3)+1 (-1)+(-3)\, \times \, 0=5. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & 1 & -3 \\
+ 0 & 3 & 2 \\
+ -1 & 1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 3 & -3 \\
+ -1 & -1 \\
+ -2 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -1 & \fbox{$5$} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 1 & -3 \\
+ 0 & 3 & 2 \\
+ -1 & 1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 3 & -3 \\
+ -1 & -1 \\
+ -2 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -1 & 5 \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0\ 3+3 (-1)+2 (-2)=-7. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & 1 & -3 \\
+ 0 & 3 & 2 \\
+ -1 & 1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 3 & -3 \\
+ -1 & -1 \\
+ -2 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -1 & 5 \\
+ \fbox{$-7$} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 1 & -3 \\
+ 0 & 3 & 2 \\
+ -1 & 1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 3 & -3 \\
+ -1 & -1 \\
+ -2 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -1 & 5 \\
+ -7 & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0 (-3)+3 (-1)+2\ 0=-3. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & 1 & -3 \\
+ 0 & 3 & 2 \\
+ -1 & 1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 3 & -3 \\
+ -1 & -1 \\
+ -2 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -1 & 5 \\
+ -7 & \fbox{$-3$} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 1 & -3 \\
+ 0 & 3 & 2 \\
+ -1 & 1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 3 & -3 \\
+ -1 & -1 \\
+ -2 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -1 & 5 \\
+ -7 & -3 \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, \times \, 3+1 (-1)+(-1)\, (-2)=-2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & 1 & -3 \\
+ 0 & 3 & 2 \\
+ -1 & 1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 3 & -3 \\
+ -1 & -1 \\
+ -2 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -1 & 5 \\
+ -7 & -3 \\
+ \fbox{$-2$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 1 & -3 \\
+ 0 & 3 & 2 \\
+ -1 & 1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 3 & -3 \\
+ -1 & -1 \\
+ -2 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -1 & 5 \\
+ -7 & -3 \\
+ -2 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, (-3)+1 (-1)+(-1)\, \times \, 0=2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ -2 & 1 & -3 \\
+ 0 & 3 & 2 \\
+ -1 & 1 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 3 & -3 \\
+ -1 & -1 \\
+ -2 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -1 & 5 \\
+ -7 & -3 \\
+ -2 & \fbox{$2$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/302.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/302.txt
new file mode 100644
index 0000000000000000000000000000000000000000..89d629c01a6b3b52315baecd74fe69a8084090ce
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/302.txt
@@ -0,0 +1,231 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ -2 & 0 & 2 \\
+ 1 & 2 & -2 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 0 \\
+ 0 \\
+ 2 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 0 & 2 \\
+ 1 & 2 & -2 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 0 \\
+ 0 \\
+ 2 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & 0 & 2 \\
+ 1 & 2 & -2 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 0 \\
+ 0 \\
+ 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 0 & 2 \\
+ 1 & 2 & -2 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 0 \\
+ 0 \\
+ 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, \times \, 0+0\ 0+2\ 2=4. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & 0 & 2 \\
+ 1 & 2 & -2 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 0 \\
+ 0 \\
+ 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$4$} \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 0 & 2 \\
+ 1 & 2 & -2 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 0 \\
+ 0 \\
+ 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 4 \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1\ 0+2\ 0+(-2)\, \times \, 2=-4. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & 0 & 2 \\
+ 1 & 2 & -2 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 0 \\
+ 0 \\
+ 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 4 \\
+ \fbox{$-4$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 0 & 2 \\
+ 1 & 2 & -2 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 0 \\
+ 0 \\
+ 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 4 \\
+ -4 \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, \times \, 0+1\ 0+2\ 2=4. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ -2 & 0 & 2 \\
+ 1 & 2 & -2 \\
+ -1 & 1 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 0 \\
+ 0 \\
+ 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 4 \\
+ -4 \\
+ \fbox{$4$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/3131.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/3131.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1ddc0c3072b77fc95221dc9b6970cf646cdd4030
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/3131.txt
@@ -0,0 +1,264 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ -2 & 0 & 0 \\
+ 1 & 2 & -2 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ -1 & 2 \\
+ 3 & -3 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 0 & 0 \\
+ 1 & 2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ -1 & 2 \\
+ 3 & -3 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 2. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 2: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & 0 & 0 \\
+ 1 & 2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ -1 & 2 \\
+ 3 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 0 & 0 \\
+ 1 & 2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ -1 & 2 \\
+ 3 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, (-1)+0 (-1)+0\ 3=2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & 0 & 0 \\
+ 1 & 2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ -1 & 2 \\
+ 3 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \fbox{$2$} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 0 & 0 \\
+ 1 & 2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ -1 & 2 \\
+ 3 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 2 & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, \times \, 3+0\ 2+0 (-3)=-6. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & 0 & 0 \\
+ 1 & 2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ -1 & 2 \\
+ 3 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 2 & \fbox{$-6$} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 0 & 0 \\
+ 1 & 2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ -1 & 2 \\
+ 3 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 2 & -6 \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1 (-1)+2 (-1)+(-2)\, \times \, 3=-9. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & 0 & 0 \\
+ 1 & 2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ -1 & 2 \\
+ 3 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 2 & -6 \\
+ \fbox{$-9$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 0 & 0 \\
+ 1 & 2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ -1 & 2 \\
+ 3 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 2 & -6 \\
+ -9 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1\ 3+2\ 2+(-2)\, (-3)=13. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ -2 & 0 & 0 \\
+ 1 & 2 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ -1 & 2 \\
+ 3 & -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 2 & -6 \\
+ -9 & \fbox{$13$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/3214.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/3214.txt
new file mode 100644
index 0000000000000000000000000000000000000000..686557c63502b8efba4afa4e74d422ed4c4e55cf
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/3214.txt
@@ -0,0 +1,362 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ -\frac{35}{16} & -\frac{21}{16} & \frac{33}{16} \\
+ \frac{3}{2} & -\frac{7}{8} & -\frac{23}{16} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ -\frac{21}{16} & -\frac{9}{4} & -\frac{43}{16} \\
+ -\frac{7}{16} & -3 & \frac{37}{16} \\
+ \frac{33}{16} & \frac{1}{8} & -\frac{17}{16} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{35}{16} & -\frac{21}{16} & \frac{33}{16} \\
+ \frac{3}{2} & -\frac{7}{8} & -\frac{23}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{21}{16} & -\frac{9}{4} & -\frac{43}{16} \\
+ -\frac{7}{16} & -3 & \frac{37}{16} \\
+ \frac{33}{16} & \frac{1}{8} & -\frac{17}{16} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{35}{16} & -\frac{21}{16} & \frac{33}{16} \\
+ \frac{3}{2} & -\frac{7}{8} & -\frac{23}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{21}{16} & -\frac{9}{4} & -\frac{43}{16} \\
+ -\frac{7}{16} & -3 & \frac{37}{16} \\
+ \frac{33}{16} & \frac{1}{8} & -\frac{17}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{35}{16} & -\frac{21}{16} & \frac{33}{16} \\
+ \frac{3}{2} & -\frac{7}{8} & -\frac{23}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{21}{16} & -\frac{9}{4} & -\frac{43}{16} \\
+ -\frac{7}{16} & -3 & \frac{37}{16} \\
+ \frac{33}{16} & \frac{1}{8} & -\frac{17}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{35}{16}\right)\, \left(-\frac{21}{16}\right)+\left(-\frac{21}{16}\right)\, \left(-\frac{7}{16}\right)+\frac{33\ 33}{16\ 16}=\frac{1971}{256}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{35}{16} & -\frac{21}{16} & \frac{33}{16} \\
+ \frac{3}{2} & -\frac{7}{8} & -\frac{23}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{21}{16} & -\frac{9}{4} & -\frac{43}{16} \\
+ -\frac{7}{16} & -3 & \frac{37}{16} \\
+ \frac{33}{16} & \frac{1}{8} & -\frac{17}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$\frac{1971}{256}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{35}{16} & -\frac{21}{16} & \frac{33}{16} \\
+ \frac{3}{2} & -\frac{7}{8} & -\frac{23}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{21}{16} & -\frac{9}{4} & -\frac{43}{16} \\
+ -\frac{7}{16} & -3 & \frac{37}{16} \\
+ \frac{33}{16} & \frac{1}{8} & -\frac{17}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{1971}{256} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{35}{16}\right)\, \left(-\frac{9}{4}\right)+\left(-\frac{21}{16}\right)\, (-3)+\frac{33}{16\ 8}=\frac{1167}{128}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{35}{16} & -\frac{21}{16} & \frac{33}{16} \\
+ \frac{3}{2} & -\frac{7}{8} & -\frac{23}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{21}{16} & -\frac{9}{4} & -\frac{43}{16} \\
+ -\frac{7}{16} & -3 & \frac{37}{16} \\
+ \frac{33}{16} & \frac{1}{8} & -\frac{17}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{1971}{256} & \fbox{$\frac{1167}{128}$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{35}{16} & -\frac{21}{16} & \frac{33}{16} \\
+ \frac{3}{2} & -\frac{7}{8} & -\frac{23}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{21}{16} & -\frac{9}{4} & -\frac{43}{16} \\
+ -\frac{7}{16} & -3 & \frac{37}{16} \\
+ \frac{33}{16} & \frac{1}{8} & -\frac{17}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{1971}{256} & \frac{1167}{128} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{35}{16}\right)\, \left(-\frac{43}{16}\right)+\left(-\frac{21}{16}\right)\, \times \, \frac{37}{16}+\frac{33 (-17)}{16\ 16}=\frac{167}{256}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{35}{16} & -\frac{21}{16} & \frac{33}{16} \\
+ \frac{3}{2} & -\frac{7}{8} & -\frac{23}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{21}{16} & -\frac{9}{4} & -\frac{43}{16} \\
+ -\frac{7}{16} & -3 & \frac{37}{16} \\
+ \frac{33}{16} & \frac{1}{8} & -\frac{17}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{1971}{256} & \frac{1167}{128} & \fbox{$\frac{167}{256}$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{35}{16} & -\frac{21}{16} & \frac{33}{16} \\
+ \frac{3}{2} & -\frac{7}{8} & -\frac{23}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{21}{16} & -\frac{9}{4} & -\frac{43}{16} \\
+ -\frac{7}{16} & -3 & \frac{37}{16} \\
+ \frac{33}{16} & \frac{1}{8} & -\frac{17}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{1971}{256} & \frac{1167}{128} & \frac{167}{256} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{3 (-21)}{2\ 16}+\left(-\frac{7}{8}\right)\, \left(-\frac{7}{16}\right)+\left(-\frac{23}{16}\right)\, \times \, \frac{33}{16}=-\frac{1165}{256}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{35}{16} & -\frac{21}{16} & \frac{33}{16} \\
+ \frac{3}{2} & -\frac{7}{8} & -\frac{23}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{21}{16} & -\frac{9}{4} & -\frac{43}{16} \\
+ -\frac{7}{16} & -3 & \frac{37}{16} \\
+ \frac{33}{16} & \frac{1}{8} & -\frac{17}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{1971}{256} & \frac{1167}{128} & \frac{167}{256} \\
+ \fbox{$-\frac{1165}{256}$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{35}{16} & -\frac{21}{16} & \frac{33}{16} \\
+ \frac{3}{2} & -\frac{7}{8} & -\frac{23}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{21}{16} & -\frac{9}{4} & -\frac{43}{16} \\
+ -\frac{7}{16} & -3 & \frac{37}{16} \\
+ \frac{33}{16} & \frac{1}{8} & -\frac{17}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{1971}{256} & \frac{1167}{128} & \frac{167}{256} \\
+ -\frac{1165}{256} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{3 (-9)}{2\ 4}+\left(-\frac{7}{8}\right)\, (-3)+\left(-\frac{23}{16}\right)\, \times \, \frac{1}{8}=-\frac{119}{128}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{35}{16} & -\frac{21}{16} & \frac{33}{16} \\
+ \frac{3}{2} & -\frac{7}{8} & -\frac{23}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{21}{16} & -\frac{9}{4} & -\frac{43}{16} \\
+ -\frac{7}{16} & -3 & \frac{37}{16} \\
+ \frac{33}{16} & \frac{1}{8} & -\frac{17}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{1971}{256} & \frac{1167}{128} & \frac{167}{256} \\
+ -\frac{1165}{256} & \fbox{$-\frac{119}{128}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{35}{16} & -\frac{21}{16} & \frac{33}{16} \\
+ \frac{3}{2} & -\frac{7}{8} & -\frac{23}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{21}{16} & -\frac{9}{4} & -\frac{43}{16} \\
+ -\frac{7}{16} & -3 & \frac{37}{16} \\
+ \frac{33}{16} & \frac{1}{8} & -\frac{17}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{1971}{256} & \frac{1167}{128} & \frac{167}{256} \\
+ -\frac{1165}{256} & -\frac{119}{128} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{3 (-43)}{2\ 16}+\left(-\frac{7}{8}\right)\, \times \, \frac{37}{16}+\left(-\frac{23}{16}\right)\, \left(-\frac{17}{16}\right)=-\frac{1159}{256}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ -\frac{35}{16} & -\frac{21}{16} & \frac{33}{16} \\
+ \frac{3}{2} & -\frac{7}{8} & -\frac{23}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{21}{16} & -\frac{9}{4} & -\frac{43}{16} \\
+ -\frac{7}{16} & -3 & \frac{37}{16} \\
+ \frac{33}{16} & \frac{1}{8} & -\frac{17}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{1971}{256} & \frac{1167}{128} & \frac{167}{256} \\
+ -\frac{1165}{256} & -\frac{119}{128} & \fbox{$-\frac{1159}{256}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/3320.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/3320.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bb97c394e88e7c5c84ce52c76eec51af3f6d4671
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/3320.txt
@@ -0,0 +1,362 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ 0 & -\frac{5}{2} & 0 \\
+ \frac{3}{2} & 3 & 0 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ -1 & -\frac{3}{2} & -1 \\
+ 2 & \frac{5}{2} & -\frac{1}{2} \\
+ -2 & -\frac{3}{2} & -1 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ 0 & -\frac{5}{2} & 0 \\
+ \frac{3}{2} & 3 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -\frac{3}{2} & -1 \\
+ 2 & \frac{5}{2} & -\frac{1}{2} \\
+ -2 & -\frac{3}{2} & -1 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 0 & -\frac{5}{2} & 0 \\
+ \frac{3}{2} & 3 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -\frac{3}{2} & -1 \\
+ 2 & \frac{5}{2} & -\frac{1}{2} \\
+ -2 & -\frac{3}{2} & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 0 & -\frac{5}{2} & 0 \\
+ \frac{3}{2} & 3 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -\frac{3}{2} & -1 \\
+ 2 & \frac{5}{2} & -\frac{1}{2} \\
+ -2 & -\frac{3}{2} & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0 (-1)+\left(-\frac{5}{2}\right)\, \times \, 2+0 (-2)=-5. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 0 & -\frac{5}{2} & 0 \\
+ \frac{3}{2} & 3 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -\frac{3}{2} & -1 \\
+ 2 & \frac{5}{2} & -\frac{1}{2} \\
+ -2 & -\frac{3}{2} & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$-5$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 0 & -\frac{5}{2} & 0 \\
+ \frac{3}{2} & 3 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -\frac{3}{2} & -1 \\
+ 2 & \frac{5}{2} & -\frac{1}{2} \\
+ -2 & -\frac{3}{2} & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{0 (-3)}{2}+\left(-\frac{5}{2}\right)\, \times \, \frac{5}{2}+\frac{0 (-3)}{2}=-\frac{25}{4}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 0 & -\frac{5}{2} & 0 \\
+ \frac{3}{2} & 3 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -\frac{3}{2} & -1 \\
+ 2 & \frac{5}{2} & -\frac{1}{2} \\
+ -2 & -\frac{3}{2} & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & \fbox{$-\frac{25}{4}$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 0 & -\frac{5}{2} & 0 \\
+ \frac{3}{2} & 3 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -\frac{3}{2} & -1 \\
+ 2 & \frac{5}{2} & -\frac{1}{2} \\
+ -2 & -\frac{3}{2} & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -\frac{25}{4} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0 (-1)+\frac{5}{2\ 2}+0 (-1)=\frac{5}{4}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 0 & -\frac{5}{2} & 0 \\
+ \frac{3}{2} & 3 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -\frac{3}{2} & -1 \\
+ 2 & \frac{5}{2} & -\frac{1}{2} \\
+ -2 & -\frac{3}{2} & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -\frac{25}{4} & \fbox{$\frac{5}{4}$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 0 & -\frac{5}{2} & 0 \\
+ \frac{3}{2} & 3 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -\frac{3}{2} & -1 \\
+ 2 & \frac{5}{2} & -\frac{1}{2} \\
+ -2 & -\frac{3}{2} & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -\frac{25}{4} & \frac{5}{4} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{3 (-1)}{2}+3\ 2+0 (-2)=\frac{9}{2}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 0 & -\frac{5}{2} & 0 \\
+ \frac{3}{2} & 3 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -\frac{3}{2} & -1 \\
+ 2 & \frac{5}{2} & -\frac{1}{2} \\
+ -2 & -\frac{3}{2} & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -\frac{25}{4} & \frac{5}{4} \\
+ \fbox{$\frac{9}{2}$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 0 & -\frac{5}{2} & 0 \\
+ \frac{3}{2} & 3 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -\frac{3}{2} & -1 \\
+ 2 & \frac{5}{2} & -\frac{1}{2} \\
+ -2 & -\frac{3}{2} & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -\frac{25}{4} & \frac{5}{4} \\
+ \frac{9}{2} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{3 (-3)}{2\ 2}+\frac{3\ 5}{2}+\frac{0 (-3)}{2}=\frac{21}{4}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 0 & -\frac{5}{2} & 0 \\
+ \frac{3}{2} & 3 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -\frac{3}{2} & -1 \\
+ 2 & \frac{5}{2} & -\frac{1}{2} \\
+ -2 & -\frac{3}{2} & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -\frac{25}{4} & \frac{5}{4} \\
+ \frac{9}{2} & \fbox{$\frac{21}{4}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 0 & -\frac{5}{2} & 0 \\
+ \frac{3}{2} & 3 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -\frac{3}{2} & -1 \\
+ 2 & \frac{5}{2} & -\frac{1}{2} \\
+ -2 & -\frac{3}{2} & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -\frac{25}{4} & \frac{5}{4} \\
+ \frac{9}{2} & \frac{21}{4} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{3 (-1)}{2}+\frac{1}{2} (-3)+0 (-1)=-3. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ 0 & -\frac{5}{2} & 0 \\
+ \frac{3}{2} & 3 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -1 & -\frac{3}{2} & -1 \\
+ 2 & \frac{5}{2} & -\frac{1}{2} \\
+ -2 & -\frac{3}{2} & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -\frac{25}{4} & \frac{5}{4} \\
+ \frac{9}{2} & \frac{21}{4} & \fbox{$-3$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/3336.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/3336.txt
new file mode 100644
index 0000000000000000000000000000000000000000..359aff6f2124d3ef7bc9a6015660d0a51fdd9268
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/3336.txt
@@ -0,0 +1,390 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ \frac{5}{9} & -\frac{4}{3} & -\frac{2}{3} \\
+ \frac{1}{3} & -\frac{22}{9} & 3 \\
+ -\frac{1}{3} & \frac{8}{3} & \frac{20}{9} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{cc}
+ \frac{26}{9} & -\frac{7}{3} \\
+ 2 & -\frac{7}{9} \\
+ -\frac{1}{9} & \frac{13}{9} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{9} & -\frac{4}{3} & -\frac{2}{3} \\
+ \frac{1}{3} & -\frac{22}{9} & 3 \\
+ -\frac{1}{3} & \frac{8}{3} & \frac{20}{9} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{26}{9} & -\frac{7}{3} \\
+ 2 & -\frac{7}{9} \\
+ -\frac{1}{9} & \frac{13}{9} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 2. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 2: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{9} & -\frac{4}{3} & -\frac{2}{3} \\
+ \frac{1}{3} & -\frac{22}{9} & 3 \\
+ -\frac{1}{3} & \frac{8}{3} & \frac{20}{9} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{26}{9} & -\frac{7}{3} \\
+ 2 & -\frac{7}{9} \\
+ -\frac{1}{9} & \frac{13}{9} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{9} & -\frac{4}{3} & -\frac{2}{3} \\
+ \frac{1}{3} & -\frac{22}{9} & 3 \\
+ -\frac{1}{3} & \frac{8}{3} & \frac{20}{9} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{26}{9} & -\frac{7}{3} \\
+ 2 & -\frac{7}{9} \\
+ -\frac{1}{9} & \frac{13}{9} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{5\ 26}{9\ 9}+\left(-\frac{4}{3}\right)\, \times \, 2+\frac{2}{3\ 9}=-\frac{80}{81}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{9} & -\frac{4}{3} & -\frac{2}{3} \\
+ \frac{1}{3} & -\frac{22}{9} & 3 \\
+ -\frac{1}{3} & \frac{8}{3} & \frac{20}{9} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{26}{9} & -\frac{7}{3} \\
+ 2 & -\frac{7}{9} \\
+ -\frac{1}{9} & \frac{13}{9} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \fbox{$-\frac{80}{81}$} & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{9} & -\frac{4}{3} & -\frac{2}{3} \\
+ \frac{1}{3} & -\frac{22}{9} & 3 \\
+ -\frac{1}{3} & \frac{8}{3} & \frac{20}{9} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{26}{9} & -\frac{7}{3} \\
+ 2 & -\frac{7}{9} \\
+ -\frac{1}{9} & \frac{13}{9} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{80}{81} & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{5 (-7)}{9\ 3}+\left(-\frac{4}{3}\right)\, \left(-\frac{7}{9}\right)+\left(-\frac{2}{3}\right)\, \times \, \frac{13}{9}=-\frac{11}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{9} & -\frac{4}{3} & -\frac{2}{3} \\
+ \frac{1}{3} & -\frac{22}{9} & 3 \\
+ -\frac{1}{3} & \frac{8}{3} & \frac{20}{9} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{26}{9} & -\frac{7}{3} \\
+ 2 & -\frac{7}{9} \\
+ -\frac{1}{9} & \frac{13}{9} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{80}{81} & \fbox{$-\frac{11}{9}$} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{9} & -\frac{4}{3} & -\frac{2}{3} \\
+ \frac{1}{3} & -\frac{22}{9} & 3 \\
+ -\frac{1}{3} & \frac{8}{3} & \frac{20}{9} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{26}{9} & -\frac{7}{3} \\
+ 2 & -\frac{7}{9} \\
+ -\frac{1}{9} & \frac{13}{9} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{80}{81} & -\frac{11}{9} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{26}{3\ 9}+\left(-\frac{22}{9}\right)\, \times \, 2+\frac{1}{9} (-3)=-\frac{115}{27}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{9} & -\frac{4}{3} & -\frac{2}{3} \\
+ \frac{1}{3} & -\frac{22}{9} & 3 \\
+ -\frac{1}{3} & \frac{8}{3} & \frac{20}{9} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{26}{9} & -\frac{7}{3} \\
+ 2 & -\frac{7}{9} \\
+ -\frac{1}{9} & \frac{13}{9} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{80}{81} & -\frac{11}{9} \\
+ \fbox{$-\frac{115}{27}$} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{9} & -\frac{4}{3} & -\frac{2}{3} \\
+ \frac{1}{3} & -\frac{22}{9} & 3 \\
+ -\frac{1}{3} & \frac{8}{3} & \frac{20}{9} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{26}{9} & -\frac{7}{3} \\
+ 2 & -\frac{7}{9} \\
+ -\frac{1}{9} & \frac{13}{9} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{80}{81} & -\frac{11}{9} \\
+ -\frac{115}{27} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }-\frac{7}{3\ 3}+\left(-\frac{22}{9}\right)\, \left(-\frac{7}{9}\right)+\frac{3\ 13}{9}=\frac{442}{81}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{9} & -\frac{4}{3} & -\frac{2}{3} \\
+ \frac{1}{3} & -\frac{22}{9} & 3 \\
+ -\frac{1}{3} & \frac{8}{3} & \frac{20}{9} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{26}{9} & -\frac{7}{3} \\
+ 2 & -\frac{7}{9} \\
+ -\frac{1}{9} & \frac{13}{9} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{80}{81} & -\frac{11}{9} \\
+ -\frac{115}{27} & \fbox{$\frac{442}{81}$} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{9} & -\frac{4}{3} & -\frac{2}{3} \\
+ \frac{1}{3} & -\frac{22}{9} & 3 \\
+ -\frac{1}{3} & \frac{8}{3} & \frac{20}{9} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{26}{9} & -\frac{7}{3} \\
+ 2 & -\frac{7}{9} \\
+ -\frac{1}{9} & \frac{13}{9} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{80}{81} & -\frac{11}{9} \\
+ -\frac{115}{27} & \frac{442}{81} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{3} \left(-\frac{26}{9}\right)+\frac{8\ 2}{3}+\frac{1}{9} \left(-\frac{20}{9}\right)=\frac{334}{81}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{9} & -\frac{4}{3} & -\frac{2}{3} \\
+ \frac{1}{3} & -\frac{22}{9} & 3 \\
+ -\frac{1}{3} & \frac{8}{3} & \frac{20}{9} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{26}{9} & -\frac{7}{3} \\
+ 2 & -\frac{7}{9} \\
+ -\frac{1}{9} & \frac{13}{9} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{80}{81} & -\frac{11}{9} \\
+ -\frac{115}{27} & \frac{442}{81} \\
+ \fbox{$\frac{334}{81}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{5}{9} & -\frac{4}{3} & -\frac{2}{3} \\
+ \frac{1}{3} & -\frac{22}{9} & 3 \\
+ -\frac{1}{3} & \frac{8}{3} & \frac{20}{9} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{26}{9} & -\frac{7}{3} \\
+ 2 & -\frac{7}{9} \\
+ -\frac{1}{9} & \frac{13}{9} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{80}{81} & -\frac{11}{9} \\
+ -\frac{115}{27} & \frac{442}{81} \\
+ \frac{334}{81} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{7}{3\ 3}+\frac{8 (-7)}{3\ 9}+\frac{20\ 13}{9\ 9}=\frac{155}{81}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ \frac{5}{9} & -\frac{4}{3} & -\frac{2}{3} \\
+ \frac{1}{3} & -\frac{22}{9} & 3 \\
+ -\frac{1}{3} & \frac{8}{3} & \frac{20}{9} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{26}{9} & -\frac{7}{3} \\
+ 2 & -\frac{7}{9} \\
+ -\frac{1}{9} & \frac{13}{9} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{80}{81} & -\frac{11}{9} \\
+ -\frac{115}{27} & \frac{442}{81} \\
+ \frac{334}{81} & \fbox{$\frac{155}{81}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/3408.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/3408.txt
new file mode 100644
index 0000000000000000000000000000000000000000..05b4d5042415fb9a445cc0a06a426f97d2416b4d
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/3408.txt
@@ -0,0 +1,347 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ \frac{3}{2} & -\frac{11}{10} \\
+ \frac{19}{10} & -\frac{2}{5} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ -\frac{1}{10} & -2 & -\frac{11}{5} \\
+ \frac{9}{5} & 3 & \frac{21}{10} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{2} & -\frac{11}{10} \\
+ \frac{19}{10} & -\frac{2}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{10} & -2 & -\frac{11}{5} \\
+ \frac{9}{5} & 3 & \frac{21}{10} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{2} & -\frac{11}{10} \\
+ \frac{19}{10} & -\frac{2}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{10} & -2 & -\frac{11}{5} \\
+ \frac{9}{5} & 3 & \frac{21}{10} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{2} & -\frac{11}{10} \\
+ \frac{19}{10} & -\frac{2}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{10} & -2 & -\frac{11}{5} \\
+ \frac{9}{5} & 3 & \frac{21}{10} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{10} \left(-\frac{3}{2}\right)+\left(-\frac{11}{10}\right)\, \times \, \frac{9}{5}=-\frac{213}{100}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{2} & -\frac{11}{10} \\
+ \frac{19}{10} & -\frac{2}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{10} & -2 & -\frac{11}{5} \\
+ \frac{9}{5} & 3 & \frac{21}{10} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$-\frac{213}{100}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{2} & -\frac{11}{10} \\
+ \frac{19}{10} & -\frac{2}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{10} & -2 & -\frac{11}{5} \\
+ \frac{9}{5} & 3 & \frac{21}{10} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{213}{100} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{3 (-2)}{2}+\left(-\frac{11}{10}\right)\, \times \, 3=-\frac{63}{10}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{2} & -\frac{11}{10} \\
+ \frac{19}{10} & -\frac{2}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{10} & -2 & -\frac{11}{5} \\
+ \frac{9}{5} & 3 & \frac{21}{10} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{213}{100} & \fbox{$-\frac{63}{10}$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{2} & -\frac{11}{10} \\
+ \frac{19}{10} & -\frac{2}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{10} & -2 & -\frac{11}{5} \\
+ \frac{9}{5} & 3 & \frac{21}{10} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{213}{100} & -\frac{63}{10} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{3 (-11)}{2\ 5}+\left(-\frac{11}{10}\right)\, \times \, \frac{21}{10}=-\frac{561}{100}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{2} & -\frac{11}{10} \\
+ \frac{19}{10} & -\frac{2}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{10} & -2 & -\frac{11}{5} \\
+ \frac{9}{5} & 3 & \frac{21}{10} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{213}{100} & -\frac{63}{10} & \fbox{$-\frac{561}{100}$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{2} & -\frac{11}{10} \\
+ \frac{19}{10} & -\frac{2}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{10} & -2 & -\frac{11}{5} \\
+ \frac{9}{5} & 3 & \frac{21}{10} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{213}{100} & -\frac{63}{10} & -\frac{561}{100} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{10} \left(-\frac{19}{10}\right)+\left(-\frac{2}{5}\right)\, \times \, \frac{9}{5}=-\frac{91}{100}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{2} & -\frac{11}{10} \\
+ \frac{19}{10} & -\frac{2}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{10} & -2 & -\frac{11}{5} \\
+ \frac{9}{5} & 3 & \frac{21}{10} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{213}{100} & -\frac{63}{10} & -\frac{561}{100} \\
+ \fbox{$-\frac{91}{100}$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{2} & -\frac{11}{10} \\
+ \frac{19}{10} & -\frac{2}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{10} & -2 & -\frac{11}{5} \\
+ \frac{9}{5} & 3 & \frac{21}{10} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{213}{100} & -\frac{63}{10} & -\frac{561}{100} \\
+ -\frac{91}{100} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{19 (-2)}{10}+\left(-\frac{2}{5}\right)\, \times \, 3=-5. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{2} & -\frac{11}{10} \\
+ \frac{19}{10} & -\frac{2}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{10} & -2 & -\frac{11}{5} \\
+ \frac{9}{5} & 3 & \frac{21}{10} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{213}{100} & -\frac{63}{10} & -\frac{561}{100} \\
+ -\frac{91}{100} & \fbox{$-5$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{2} & -\frac{11}{10} \\
+ \frac{19}{10} & -\frac{2}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{10} & -2 & -\frac{11}{5} \\
+ \frac{9}{5} & 3 & \frac{21}{10} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{213}{100} & -\frac{63}{10} & -\frac{561}{100} \\
+ -\frac{91}{100} & -5 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{19 (-11)}{10\ 5}+\left(-\frac{2}{5}\right)\, \times \, \frac{21}{10}=-\frac{251}{50}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ \frac{3}{2} & -\frac{11}{10} \\
+ \frac{19}{10} & -\frac{2}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{1}{10} & -2 & -\frac{11}{5} \\
+ \frac{9}{5} & 3 & \frac{21}{10} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{213}{100} & -\frac{63}{10} & -\frac{561}{100} \\
+ -\frac{91}{100} & -5 & \fbox{$-\frac{251}{50}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/3493.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/3493.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e963c3d3ef615f68bb08ed83bfa273c85751b2f1
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/3493.txt
@@ -0,0 +1,375 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ 2 & \frac{9}{5} \\
+ -\frac{17}{10} & -\frac{12}{5} \\
+ -\frac{3}{10} & -\frac{9}{10} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{3}{2} \\
+ -\frac{5}{2} & \frac{9}{5} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{9}{5} \\
+ -\frac{17}{10} & -\frac{12}{5} \\
+ -\frac{3}{10} & -\frac{9}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{3}{2} \\
+ -\frac{5}{2} & \frac{9}{5} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 2. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 2: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{9}{5} \\
+ -\frac{17}{10} & -\frac{12}{5} \\
+ -\frac{3}{10} & -\frac{9}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{3}{2} \\
+ -\frac{5}{2} & \frac{9}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{9}{5} \\
+ -\frac{17}{10} & -\frac{12}{5} \\
+ -\frac{3}{10} & -\frac{9}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{3}{2} \\
+ -\frac{5}{2} & \frac{9}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2}{5}+\frac{9 (-5)}{5\ 2}=-\frac{41}{10}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{9}{5} \\
+ -\frac{17}{10} & -\frac{12}{5} \\
+ -\frac{3}{10} & -\frac{9}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{3}{2} \\
+ -\frac{5}{2} & \frac{9}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \fbox{$-\frac{41}{10}$} & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{9}{5} \\
+ -\frac{17}{10} & -\frac{12}{5} \\
+ -\frac{3}{10} & -\frac{9}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{3}{2} \\
+ -\frac{5}{2} & \frac{9}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{41}{10} & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2\ 3}{2}+\frac{9\ 9}{5\ 5}=\frac{156}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{9}{5} \\
+ -\frac{17}{10} & -\frac{12}{5} \\
+ -\frac{3}{10} & -\frac{9}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{3}{2} \\
+ -\frac{5}{2} & \frac{9}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{41}{10} & \fbox{$\frac{156}{25}$} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{9}{5} \\
+ -\frac{17}{10} & -\frac{12}{5} \\
+ -\frac{3}{10} & -\frac{9}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{3}{2} \\
+ -\frac{5}{2} & \frac{9}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{41}{10} & \frac{156}{25} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{17}{10}\right)\, \times \, \frac{1}{5}+\left(-\frac{12}{5}\right)\, \left(-\frac{5}{2}\right)=\frac{283}{50}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{9}{5} \\
+ -\frac{17}{10} & -\frac{12}{5} \\
+ -\frac{3}{10} & -\frac{9}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{3}{2} \\
+ -\frac{5}{2} & \frac{9}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{41}{10} & \frac{156}{25} \\
+ \fbox{$\frac{283}{50}$} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{9}{5} \\
+ -\frac{17}{10} & -\frac{12}{5} \\
+ -\frac{3}{10} & -\frac{9}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{3}{2} \\
+ -\frac{5}{2} & \frac{9}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{41}{10} & \frac{156}{25} \\
+ \frac{283}{50} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{17}{10}\right)\, \times \, \frac{3}{2}+\left(-\frac{12}{5}\right)\, \times \, \frac{9}{5}=-\frac{687}{100}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{9}{5} \\
+ -\frac{17}{10} & -\frac{12}{5} \\
+ -\frac{3}{10} & -\frac{9}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{3}{2} \\
+ -\frac{5}{2} & \frac{9}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{41}{10} & \frac{156}{25} \\
+ \frac{283}{50} & \fbox{$-\frac{687}{100}$} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{9}{5} \\
+ -\frac{17}{10} & -\frac{12}{5} \\
+ -\frac{3}{10} & -\frac{9}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{3}{2} \\
+ -\frac{5}{2} & \frac{9}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{41}{10} & \frac{156}{25} \\
+ \frac{283}{50} & -\frac{687}{100} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{3}{10}\right)\, \times \, \frac{1}{5}+\left(-\frac{9}{10}\right)\, \left(-\frac{5}{2}\right)=\frac{219}{100}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{9}{5} \\
+ -\frac{17}{10} & -\frac{12}{5} \\
+ -\frac{3}{10} & -\frac{9}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{3}{2} \\
+ -\frac{5}{2} & \frac{9}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{41}{10} & \frac{156}{25} \\
+ \frac{283}{50} & -\frac{687}{100} \\
+ \fbox{$\frac{219}{100}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & \frac{9}{5} \\
+ -\frac{17}{10} & -\frac{12}{5} \\
+ -\frac{3}{10} & -\frac{9}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{3}{2} \\
+ -\frac{5}{2} & \frac{9}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{41}{10} & \frac{156}{25} \\
+ \frac{283}{50} & -\frac{687}{100} \\
+ \frac{219}{100} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{3}{10}\right)\, \times \, \frac{3}{2}+\left(-\frac{9}{10}\right)\, \times \, \frac{9}{5}=-\frac{207}{100}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ 2 & \frac{9}{5} \\
+ -\frac{17}{10} & -\frac{12}{5} \\
+ -\frac{3}{10} & -\frac{9}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{3}{2} \\
+ -\frac{5}{2} & \frac{9}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{41}{10} & \frac{156}{25} \\
+ \frac{283}{50} & -\frac{687}{100} \\
+ \frac{219}{100} & \fbox{$-\frac{207}{100}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/3646.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/3646.txt
new file mode 100644
index 0000000000000000000000000000000000000000..89a92bfc4b4a812e42467177d337abecabf7645b
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/3646.txt
@@ -0,0 +1,375 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{6}{5} \\
+ 3 & -\frac{13}{5} \\
+ -\frac{9}{5} & \frac{7}{5} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{cc}
+ -\frac{8}{5} & -\frac{11}{5} \\
+ -\frac{14}{5} & \frac{14}{5} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{6}{5} \\
+ 3 & -\frac{13}{5} \\
+ -\frac{9}{5} & \frac{7}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{8}{5} & -\frac{11}{5} \\
+ -\frac{14}{5} & \frac{14}{5} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 2. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 2: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{6}{5} \\
+ 3 & -\frac{13}{5} \\
+ -\frac{9}{5} & \frac{7}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{8}{5} & -\frac{11}{5} \\
+ -\frac{14}{5} & \frac{14}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{6}{5} \\
+ 3 & -\frac{13}{5} \\
+ -\frac{9}{5} & \frac{7}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{8}{5} & -\frac{11}{5} \\
+ -\frac{14}{5} & \frac{14}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{3 (-8)}{5\ 5}+\left(-\frac{6}{5}\right)\, \left(-\frac{14}{5}\right)=\frac{12}{5}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{6}{5} \\
+ 3 & -\frac{13}{5} \\
+ -\frac{9}{5} & \frac{7}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{8}{5} & -\frac{11}{5} \\
+ -\frac{14}{5} & \frac{14}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \fbox{$\frac{12}{5}$} & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{6}{5} \\
+ 3 & -\frac{13}{5} \\
+ -\frac{9}{5} & \frac{7}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{8}{5} & -\frac{11}{5} \\
+ -\frac{14}{5} & \frac{14}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{12}{5} & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{3 (-11)}{5\ 5}+\left(-\frac{6}{5}\right)\, \times \, \frac{14}{5}=-\frac{117}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{6}{5} \\
+ 3 & -\frac{13}{5} \\
+ -\frac{9}{5} & \frac{7}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{8}{5} & -\frac{11}{5} \\
+ -\frac{14}{5} & \frac{14}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{12}{5} & \fbox{$-\frac{117}{25}$} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{6}{5} \\
+ 3 & -\frac{13}{5} \\
+ -\frac{9}{5} & \frac{7}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{8}{5} & -\frac{11}{5} \\
+ -\frac{14}{5} & \frac{14}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{12}{5} & -\frac{117}{25} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{3 (-8)}{5}+\left(-\frac{13}{5}\right)\, \left(-\frac{14}{5}\right)=\frac{62}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{6}{5} \\
+ 3 & -\frac{13}{5} \\
+ -\frac{9}{5} & \frac{7}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{8}{5} & -\frac{11}{5} \\
+ -\frac{14}{5} & \frac{14}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{12}{5} & -\frac{117}{25} \\
+ \fbox{$\frac{62}{25}$} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{6}{5} \\
+ 3 & -\frac{13}{5} \\
+ -\frac{9}{5} & \frac{7}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{8}{5} & -\frac{11}{5} \\
+ -\frac{14}{5} & \frac{14}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{12}{5} & -\frac{117}{25} \\
+ \frac{62}{25} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{3 (-11)}{5}+\left(-\frac{13}{5}\right)\, \times \, \frac{14}{5}=-\frac{347}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{6}{5} \\
+ 3 & -\frac{13}{5} \\
+ -\frac{9}{5} & \frac{7}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{8}{5} & -\frac{11}{5} \\
+ -\frac{14}{5} & \frac{14}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{12}{5} & -\frac{117}{25} \\
+ \frac{62}{25} & \fbox{$-\frac{347}{25}$} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{6}{5} \\
+ 3 & -\frac{13}{5} \\
+ -\frac{9}{5} & \frac{7}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{8}{5} & -\frac{11}{5} \\
+ -\frac{14}{5} & \frac{14}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{12}{5} & -\frac{117}{25} \\
+ \frac{62}{25} & -\frac{347}{25} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{9}{5}\right)\, \left(-\frac{8}{5}\right)+\frac{7 (-14)}{5\ 5}=-\frac{26}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{6}{5} \\
+ 3 & -\frac{13}{5} \\
+ -\frac{9}{5} & \frac{7}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{8}{5} & -\frac{11}{5} \\
+ -\frac{14}{5} & \frac{14}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{12}{5} & -\frac{117}{25} \\
+ \frac{62}{25} & -\frac{347}{25} \\
+ \fbox{$-\frac{26}{25}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{6}{5} \\
+ 3 & -\frac{13}{5} \\
+ -\frac{9}{5} & \frac{7}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{8}{5} & -\frac{11}{5} \\
+ -\frac{14}{5} & \frac{14}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{12}{5} & -\frac{117}{25} \\
+ \frac{62}{25} & -\frac{347}{25} \\
+ -\frac{26}{25} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{9}{5}\right)\, \left(-\frac{11}{5}\right)+\frac{7\ 14}{5\ 5}=\frac{197}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{6}{5} \\
+ 3 & -\frac{13}{5} \\
+ -\frac{9}{5} & \frac{7}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -\frac{8}{5} & -\frac{11}{5} \\
+ -\frac{14}{5} & \frac{14}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{12}{5} & -\frac{117}{25} \\
+ \frac{62}{25} & -\frac{347}{25} \\
+ -\frac{26}{25} & \fbox{$\frac{197}{25}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/3680.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/3680.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cde4e689923f8123e99cd2f6d654457606bc1105
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/3680.txt
@@ -0,0 +1,390 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ -\frac{7}{6} & \frac{5}{6} & \frac{1}{3} \\
+ \frac{2}{3} & -\frac{8}{3} & -\frac{1}{3} \\
+ \frac{8}{3} & -\frac{13}{6} & 1 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{cc}
+ \frac{4}{3} & -1 \\
+ -\frac{11}{6} & -\frac{5}{6} \\
+ -\frac{2}{3} & \frac{11}{6} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{6} & \frac{5}{6} & \frac{1}{3} \\
+ \frac{2}{3} & -\frac{8}{3} & -\frac{1}{3} \\
+ \frac{8}{3} & -\frac{13}{6} & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{4}{3} & -1 \\
+ -\frac{11}{6} & -\frac{5}{6} \\
+ -\frac{2}{3} & \frac{11}{6} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 2. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 2: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{6} & \frac{5}{6} & \frac{1}{3} \\
+ \frac{2}{3} & -\frac{8}{3} & -\frac{1}{3} \\
+ \frac{8}{3} & -\frac{13}{6} & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{4}{3} & -1 \\
+ -\frac{11}{6} & -\frac{5}{6} \\
+ -\frac{2}{3} & \frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{6} & \frac{5}{6} & \frac{1}{3} \\
+ \frac{2}{3} & -\frac{8}{3} & -\frac{1}{3} \\
+ \frac{8}{3} & -\frac{13}{6} & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{4}{3} & -1 \\
+ -\frac{11}{6} & -\frac{5}{6} \\
+ -\frac{2}{3} & \frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{7}{6}\right)\, \times \, \frac{4}{3}+\frac{5 (-11)}{6\ 6}-\frac{2}{3\ 3}=-\frac{119}{36}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{6} & \frac{5}{6} & \frac{1}{3} \\
+ \frac{2}{3} & -\frac{8}{3} & -\frac{1}{3} \\
+ \frac{8}{3} & -\frac{13}{6} & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{4}{3} & -1 \\
+ -\frac{11}{6} & -\frac{5}{6} \\
+ -\frac{2}{3} & \frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \fbox{$-\frac{119}{36}$} & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{6} & \frac{5}{6} & \frac{1}{3} \\
+ \frac{2}{3} & -\frac{8}{3} & -\frac{1}{3} \\
+ \frac{8}{3} & -\frac{13}{6} & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{4}{3} & -1 \\
+ -\frac{11}{6} & -\frac{5}{6} \\
+ -\frac{2}{3} & \frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{119}{36} & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{7}{6}\right)\, (-1)+\frac{5 (-5)}{6\ 6}+\frac{11}{3\ 6}=\frac{13}{12}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{6} & \frac{5}{6} & \frac{1}{3} \\
+ \frac{2}{3} & -\frac{8}{3} & -\frac{1}{3} \\
+ \frac{8}{3} & -\frac{13}{6} & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{4}{3} & -1 \\
+ -\frac{11}{6} & -\frac{5}{6} \\
+ -\frac{2}{3} & \frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{119}{36} & \fbox{$\frac{13}{12}$} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{6} & \frac{5}{6} & \frac{1}{3} \\
+ \frac{2}{3} & -\frac{8}{3} & -\frac{1}{3} \\
+ \frac{8}{3} & -\frac{13}{6} & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{4}{3} & -1 \\
+ -\frac{11}{6} & -\frac{5}{6} \\
+ -\frac{2}{3} & \frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{119}{36} & \frac{13}{12} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2\ 4}{3\ 3}+\left(-\frac{8}{3}\right)\, \left(-\frac{11}{6}\right)+\frac{2}{3\ 3}=6. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{6} & \frac{5}{6} & \frac{1}{3} \\
+ \frac{2}{3} & -\frac{8}{3} & -\frac{1}{3} \\
+ \frac{8}{3} & -\frac{13}{6} & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{4}{3} & -1 \\
+ -\frac{11}{6} & -\frac{5}{6} \\
+ -\frac{2}{3} & \frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{119}{36} & \frac{13}{12} \\
+ \fbox{$6$} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{6} & \frac{5}{6} & \frac{1}{3} \\
+ \frac{2}{3} & -\frac{8}{3} & -\frac{1}{3} \\
+ \frac{8}{3} & -\frac{13}{6} & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{4}{3} & -1 \\
+ -\frac{11}{6} & -\frac{5}{6} \\
+ -\frac{2}{3} & \frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{119}{36} & \frac{13}{12} \\
+ 6 & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2 (-1)}{3}+\left(-\frac{8}{3}\right)\, \left(-\frac{5}{6}\right)+\frac{1}{3} \left(-\frac{11}{6}\right)=\frac{17}{18}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{6} & \frac{5}{6} & \frac{1}{3} \\
+ \frac{2}{3} & -\frac{8}{3} & -\frac{1}{3} \\
+ \frac{8}{3} & -\frac{13}{6} & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{4}{3} & -1 \\
+ -\frac{11}{6} & -\frac{5}{6} \\
+ -\frac{2}{3} & \frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{119}{36} & \frac{13}{12} \\
+ 6 & \fbox{$\frac{17}{18}$} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{6} & \frac{5}{6} & \frac{1}{3} \\
+ \frac{2}{3} & -\frac{8}{3} & -\frac{1}{3} \\
+ \frac{8}{3} & -\frac{13}{6} & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{4}{3} & -1 \\
+ -\frac{11}{6} & -\frac{5}{6} \\
+ -\frac{2}{3} & \frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{119}{36} & \frac{13}{12} \\
+ 6 & \frac{17}{18} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{8\ 4}{3\ 3}+\left(-\frac{13}{6}\right)\, \left(-\frac{11}{6}\right)-\frac{2}{3}=\frac{247}{36}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{6} & \frac{5}{6} & \frac{1}{3} \\
+ \frac{2}{3} & -\frac{8}{3} & -\frac{1}{3} \\
+ \frac{8}{3} & -\frac{13}{6} & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{4}{3} & -1 \\
+ -\frac{11}{6} & -\frac{5}{6} \\
+ -\frac{2}{3} & \frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{119}{36} & \frac{13}{12} \\
+ 6 & \frac{17}{18} \\
+ \fbox{$\frac{247}{36}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{6} & \frac{5}{6} & \frac{1}{3} \\
+ \frac{2}{3} & -\frac{8}{3} & -\frac{1}{3} \\
+ \frac{8}{3} & -\frac{13}{6} & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{4}{3} & -1 \\
+ -\frac{11}{6} & -\frac{5}{6} \\
+ -\frac{2}{3} & \frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{119}{36} & \frac{13}{12} \\
+ 6 & \frac{17}{18} \\
+ \frac{247}{36} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{8 (-1)}{3}+\left(-\frac{13}{6}\right)\, \left(-\frac{5}{6}\right)+\frac{11}{6}=\frac{35}{36}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ -\frac{7}{6} & \frac{5}{6} & \frac{1}{3} \\
+ \frac{2}{3} & -\frac{8}{3} & -\frac{1}{3} \\
+ \frac{8}{3} & -\frac{13}{6} & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{4}{3} & -1 \\
+ -\frac{11}{6} & -\frac{5}{6} \\
+ -\frac{2}{3} & \frac{11}{6} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -\frac{119}{36} & \frac{13}{12} \\
+ 6 & \frac{17}{18} \\
+ \frac{247}{36} & \fbox{$\frac{35}{36}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/3709.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/3709.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e1e04e54c2e0e6c87dcd5fa4c965cffc90bcd5cf
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/3709.txt
@@ -0,0 +1,347 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ -\frac{1}{3} & \frac{1}{3} \\
+ -2 & -\frac{5}{3} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ 1 & -2 & \frac{7}{3} \\
+ -\frac{1}{3} & -3 & \frac{1}{3} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{1}{3} & \frac{1}{3} \\
+ -2 & -\frac{5}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -2 & \frac{7}{3} \\
+ -\frac{1}{3} & -3 & \frac{1}{3} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{1}{3} & \frac{1}{3} \\
+ -2 & -\frac{5}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -2 & \frac{7}{3} \\
+ -\frac{1}{3} & -3 & \frac{1}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{1}{3} & \frac{1}{3} \\
+ -2 & -\frac{5}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -2 & \frac{7}{3} \\
+ -\frac{1}{3} & -3 & \frac{1}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{3} (-1)+\frac{1}{3} \left(-\frac{1}{3}\right)=-\frac{4}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{1}{3} & \frac{1}{3} \\
+ -2 & -\frac{5}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -2 & \frac{7}{3} \\
+ -\frac{1}{3} & -3 & \frac{1}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$-\frac{4}{9}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{1}{3} & \frac{1}{3} \\
+ -2 & -\frac{5}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -2 & \frac{7}{3} \\
+ -\frac{1}{3} & -3 & \frac{1}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{4}{9} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2}{3}-\frac{3}{3}=-\frac{1}{3}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{1}{3} & \frac{1}{3} \\
+ -2 & -\frac{5}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -2 & \frac{7}{3} \\
+ -\frac{1}{3} & -3 & \frac{1}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{4}{9} & \fbox{$-\frac{1}{3}$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{1}{3} & \frac{1}{3} \\
+ -2 & -\frac{5}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -2 & \frac{7}{3} \\
+ -\frac{1}{3} & -3 & \frac{1}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{4}{9} & -\frac{1}{3} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{3} \left(-\frac{7}{3}\right)+\frac{1}{3\ 3}=-\frac{2}{3}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{1}{3} & \frac{1}{3} \\
+ -2 & -\frac{5}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -2 & \frac{7}{3} \\
+ -\frac{1}{3} & -3 & \frac{1}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{4}{9} & -\frac{1}{3} & \fbox{$-\frac{2}{3}$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{1}{3} & \frac{1}{3} \\
+ -2 & -\frac{5}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -2 & \frac{7}{3} \\
+ -\frac{1}{3} & -3 & \frac{1}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{4}{9} & -\frac{1}{3} & -\frac{2}{3} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, \times \, 1+\frac{5}{3\ 3}=-\frac{13}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{1}{3} & \frac{1}{3} \\
+ -2 & -\frac{5}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -2 & \frac{7}{3} \\
+ -\frac{1}{3} & -3 & \frac{1}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{4}{9} & -\frac{1}{3} & -\frac{2}{3} \\
+ \fbox{$-\frac{13}{9}$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{1}{3} & \frac{1}{3} \\
+ -2 & -\frac{5}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -2 & \frac{7}{3} \\
+ -\frac{1}{3} & -3 & \frac{1}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{4}{9} & -\frac{1}{3} & -\frac{2}{3} \\
+ -\frac{13}{9} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, (-2)+\left(-\frac{5}{3}\right)\, (-3)=9. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{1}{3} & \frac{1}{3} \\
+ -2 & -\frac{5}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -2 & \frac{7}{3} \\
+ -\frac{1}{3} & -3 & \frac{1}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{4}{9} & -\frac{1}{3} & -\frac{2}{3} \\
+ -\frac{13}{9} & \fbox{$9$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{1}{3} & \frac{1}{3} \\
+ -2 & -\frac{5}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -2 & \frac{7}{3} \\
+ -\frac{1}{3} & -3 & \frac{1}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{4}{9} & -\frac{1}{3} & -\frac{2}{3} \\
+ -\frac{13}{9} & 9 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, \times \, \frac{7}{3}+\left(-\frac{5}{3}\right)\, \times \, \frac{1}{3}=-\frac{47}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ -\frac{1}{3} & \frac{1}{3} \\
+ -2 & -\frac{5}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -2 & \frac{7}{3} \\
+ -\frac{1}{3} & -3 & \frac{1}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{4}{9} & -\frac{1}{3} & -\frac{2}{3} \\
+ -\frac{13}{9} & 9 & \fbox{$-\frac{47}{9}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/3822.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/3822.txt
new file mode 100644
index 0000000000000000000000000000000000000000..687ff342a072e3d34771d261b501e85fed7351a0
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/3822.txt
@@ -0,0 +1,549 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ -2 & 2 & 1 \\
+ 1 & 1 & -1 \\
+ 0 & -2 & -3 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ -2 & 1 & -2 \\
+ -2 & 2 & 0 \\
+ 0 & 1 & -2 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 2 & 1 \\
+ 1 & 1 & -1 \\
+ 0 & -2 & -3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & -2 \\
+ -2 & 2 & 0 \\
+ 0 & 1 & -2 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & 2 & 1 \\
+ 1 & 1 & -1 \\
+ 0 & -2 & -3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & -2 \\
+ -2 & 2 & 0 \\
+ 0 & 1 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 2 & 1 \\
+ 1 & 1 & -1 \\
+ 0 & -2 & -3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & -2 \\
+ -2 & 2 & 0 \\
+ 0 & 1 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, (-2)+2 (-2)+1\ 0=0. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & 2 & 1 \\
+ 1 & 1 & -1 \\
+ 0 & -2 & -3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & -2 \\
+ -2 & 2 & 0 \\
+ 0 & 1 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$0$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 2 & 1 \\
+ 1 & 1 & -1 \\
+ 0 & -2 & -3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & -2 \\
+ -2 & 2 & 0 \\
+ 0 & 1 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, \times \, 1+2\ 2+1\ 1=3. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & 2 & 1 \\
+ 1 & 1 & -1 \\
+ 0 & -2 & -3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & -2 \\
+ -2 & 2 & 0 \\
+ 0 & 1 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & \fbox{$3$} & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 2 & 1 \\
+ 1 & 1 & -1 \\
+ 0 & -2 & -3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & -2 \\
+ -2 & 2 & 0 \\
+ 0 & 1 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & 3 & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, (-2)+2\ 0+1 (-2)=2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & 2 & 1 \\
+ 1 & 1 & -1 \\
+ 0 & -2 & -3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & -2 \\
+ -2 & 2 & 0 \\
+ 0 & 1 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & 3 & \fbox{$2$} \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 2 & 1 \\
+ 1 & 1 & -1 \\
+ 0 & -2 & -3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & -2 \\
+ -2 & 2 & 0 \\
+ 0 & 1 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & 3 & 2 \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1 (-2)+1 (-2)+(-1)\, \times \, 0=-4. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & 2 & 1 \\
+ 1 & 1 & -1 \\
+ 0 & -2 & -3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & -2 \\
+ -2 & 2 & 0 \\
+ 0 & 1 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & 3 & 2 \\
+ \fbox{$-4$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 2 & 1 \\
+ 1 & 1 & -1 \\
+ 0 & -2 & -3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & -2 \\
+ -2 & 2 & 0 \\
+ 0 & 1 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & 3 & 2 \\
+ -4 & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1\ 1+1\ 2+(-1)\, \times \, 1=2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & 2 & 1 \\
+ 1 & 1 & -1 \\
+ 0 & -2 & -3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & -2 \\
+ -2 & 2 & 0 \\
+ 0 & 1 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & 3 & 2 \\
+ -4 & \fbox{$2$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 2 & 1 \\
+ 1 & 1 & -1 \\
+ 0 & -2 & -3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & -2 \\
+ -2 & 2 & 0 \\
+ 0 & 1 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & 3 & 2 \\
+ -4 & 2 & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1 (-2)+1\ 0+(-1)\, (-2)=0. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & 2 & 1 \\
+ 1 & 1 & -1 \\
+ 0 & -2 & -3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & -2 \\
+ -2 & 2 & 0 \\
+ 0 & 1 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & 3 & 2 \\
+ -4 & 2 & \fbox{$0$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 2 & 1 \\
+ 1 & 1 & -1 \\
+ 0 & -2 & -3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & -2 \\
+ -2 & 2 & 0 \\
+ 0 & 1 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & 3 & 2 \\
+ -4 & 2 & 0 \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0 (-2)+(-2)\, (-2)+(-3)\, \times \, 0=4. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & 2 & 1 \\
+ 1 & 1 & -1 \\
+ 0 & -2 & -3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & -2 \\
+ -2 & 2 & 0 \\
+ 0 & 1 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & 3 & 2 \\
+ -4 & 2 & 0 \\
+ \fbox{$4$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 2 & 1 \\
+ 1 & 1 & -1 \\
+ 0 & -2 & -3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & -2 \\
+ -2 & 2 & 0 \\
+ 0 & 1 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & 3 & 2 \\
+ -4 & 2 & 0 \\
+ 4 & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0\ 1+(-2)\, \times \, 2+(-3)\, \times \, 1=-7. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -2 & 2 & 1 \\
+ 1 & 1 & -1 \\
+ 0 & -2 & -3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & -2 \\
+ -2 & 2 & 0 \\
+ 0 & 1 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & 3 & 2 \\
+ -4 & 2 & 0 \\
+ 4 & \fbox{$-7$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -2 & 2 & 1 \\
+ 1 & 1 & -1 \\
+ 0 & -2 & -3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & -2 \\
+ -2 & 2 & 0 \\
+ 0 & 1 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & 3 & 2 \\
+ -4 & 2 & 0 \\
+ 4 & -7 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0 (-2)+(-2)\, \times \, 0+(-3)\, (-2)=6. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ -2 & 2 & 1 \\
+ 1 & 1 & -1 \\
+ 0 & -2 & -3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & -2 \\
+ -2 & 2 & 0 \\
+ 0 & 1 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 0 & 3 & 2 \\
+ -4 & 2 & 0 \\
+ 4 & -7 & \fbox{$6$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/3984.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/3984.txt
new file mode 100644
index 0000000000000000000000000000000000000000..35ac9abddc6b496e651aa8758b428ea0128e62ee
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/3984.txt
@@ -0,0 +1,549 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ 2 & -\frac{1}{3} & -2 \\
+ -\frac{4}{3} & -\frac{4}{3} & -\frac{2}{3} \\
+ -\frac{4}{3} & \frac{2}{3} & \frac{1}{3} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ -\frac{8}{3} & -\frac{2}{3} & \frac{8}{3} \\
+ 1 & -\frac{2}{3} & 2 \\
+ -\frac{7}{3} & -1 & -\frac{7}{3} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{1}{3} & -2 \\
+ -\frac{4}{3} & -\frac{4}{3} & -\frac{2}{3} \\
+ -\frac{4}{3} & \frac{2}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{8}{3} & -\frac{2}{3} & \frac{8}{3} \\
+ 1 & -\frac{2}{3} & 2 \\
+ -\frac{7}{3} & -1 & -\frac{7}{3} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{1}{3} & -2 \\
+ -\frac{4}{3} & -\frac{4}{3} & -\frac{2}{3} \\
+ -\frac{4}{3} & \frac{2}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{8}{3} & -\frac{2}{3} & \frac{8}{3} \\
+ 1 & -\frac{2}{3} & 2 \\
+ -\frac{7}{3} & -1 & -\frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{1}{3} & -2 \\
+ -\frac{4}{3} & -\frac{4}{3} & -\frac{2}{3} \\
+ -\frac{4}{3} & \frac{2}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{8}{3} & -\frac{2}{3} & \frac{8}{3} \\
+ 1 & -\frac{2}{3} & 2 \\
+ -\frac{7}{3} & -1 & -\frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2 (-8)}{3}+\frac{1}{3} (-1)+(-2)\, \left(-\frac{7}{3}\right)=-1. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{1}{3} & -2 \\
+ -\frac{4}{3} & -\frac{4}{3} & -\frac{2}{3} \\
+ -\frac{4}{3} & \frac{2}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{8}{3} & -\frac{2}{3} & \frac{8}{3} \\
+ 1 & -\frac{2}{3} & 2 \\
+ -\frac{7}{3} & -1 & -\frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$-1$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{1}{3} & -2 \\
+ -\frac{4}{3} & -\frac{4}{3} & -\frac{2}{3} \\
+ -\frac{4}{3} & \frac{2}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{8}{3} & -\frac{2}{3} & \frac{8}{3} \\
+ 1 & -\frac{2}{3} & 2 \\
+ -\frac{7}{3} & -1 & -\frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -1 & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2 (-2)}{3}+\frac{2}{3\ 3}+(-2)\, (-1)=\frac{8}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{1}{3} & -2 \\
+ -\frac{4}{3} & -\frac{4}{3} & -\frac{2}{3} \\
+ -\frac{4}{3} & \frac{2}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{8}{3} & -\frac{2}{3} & \frac{8}{3} \\
+ 1 & -\frac{2}{3} & 2 \\
+ -\frac{7}{3} & -1 & -\frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -1 & \fbox{$\frac{8}{9}$} & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{1}{3} & -2 \\
+ -\frac{4}{3} & -\frac{4}{3} & -\frac{2}{3} \\
+ -\frac{4}{3} & \frac{2}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{8}{3} & -\frac{2}{3} & \frac{8}{3} \\
+ 1 & -\frac{2}{3} & 2 \\
+ -\frac{7}{3} & -1 & -\frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -1 & \frac{8}{9} & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2\ 8}{3}+\frac{1}{3} (-2)+(-2)\, \left(-\frac{7}{3}\right)=\frac{28}{3}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{1}{3} & -2 \\
+ -\frac{4}{3} & -\frac{4}{3} & -\frac{2}{3} \\
+ -\frac{4}{3} & \frac{2}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{8}{3} & -\frac{2}{3} & \frac{8}{3} \\
+ 1 & -\frac{2}{3} & 2 \\
+ -\frac{7}{3} & -1 & -\frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -1 & \frac{8}{9} & \fbox{$\frac{28}{3}$} \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{1}{3} & -2 \\
+ -\frac{4}{3} & -\frac{4}{3} & -\frac{2}{3} \\
+ -\frac{4}{3} & \frac{2}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{8}{3} & -\frac{2}{3} & \frac{8}{3} \\
+ 1 & -\frac{2}{3} & 2 \\
+ -\frac{7}{3} & -1 & -\frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -1 & \frac{8}{9} & \frac{28}{3} \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{4}{3}\right)\, \left(-\frac{8}{3}\right)+\left(-\frac{4}{3}\right)\, \times \, 1+\left(-\frac{2}{3}\right)\, \left(-\frac{7}{3}\right)=\frac{34}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{1}{3} & -2 \\
+ -\frac{4}{3} & -\frac{4}{3} & -\frac{2}{3} \\
+ -\frac{4}{3} & \frac{2}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{8}{3} & -\frac{2}{3} & \frac{8}{3} \\
+ 1 & -\frac{2}{3} & 2 \\
+ -\frac{7}{3} & -1 & -\frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -1 & \frac{8}{9} & \frac{28}{3} \\
+ \fbox{$\frac{34}{9}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{1}{3} & -2 \\
+ -\frac{4}{3} & -\frac{4}{3} & -\frac{2}{3} \\
+ -\frac{4}{3} & \frac{2}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{8}{3} & -\frac{2}{3} & \frac{8}{3} \\
+ 1 & -\frac{2}{3} & 2 \\
+ -\frac{7}{3} & -1 & -\frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -1 & \frac{8}{9} & \frac{28}{3} \\
+ \frac{34}{9} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{4}{3}\right)\, \left(-\frac{2}{3}\right)+\left(-\frac{4}{3}\right)\, \left(-\frac{2}{3}\right)+\left(-\frac{2}{3}\right)\, (-1)=\frac{22}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{1}{3} & -2 \\
+ -\frac{4}{3} & -\frac{4}{3} & -\frac{2}{3} \\
+ -\frac{4}{3} & \frac{2}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{8}{3} & -\frac{2}{3} & \frac{8}{3} \\
+ 1 & -\frac{2}{3} & 2 \\
+ -\frac{7}{3} & -1 & -\frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -1 & \frac{8}{9} & \frac{28}{3} \\
+ \frac{34}{9} & \fbox{$\frac{22}{9}$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{1}{3} & -2 \\
+ -\frac{4}{3} & -\frac{4}{3} & -\frac{2}{3} \\
+ -\frac{4}{3} & \frac{2}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{8}{3} & -\frac{2}{3} & \frac{8}{3} \\
+ 1 & -\frac{2}{3} & 2 \\
+ -\frac{7}{3} & -1 & -\frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -1 & \frac{8}{9} & \frac{28}{3} \\
+ \frac{34}{9} & \frac{22}{9} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{4}{3}\right)\, \times \, \frac{8}{3}+\left(-\frac{4}{3}\right)\, \times \, 2+\left(-\frac{2}{3}\right)\, \left(-\frac{7}{3}\right)=-\frac{14}{3}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{1}{3} & -2 \\
+ -\frac{4}{3} & -\frac{4}{3} & -\frac{2}{3} \\
+ -\frac{4}{3} & \frac{2}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{8}{3} & -\frac{2}{3} & \frac{8}{3} \\
+ 1 & -\frac{2}{3} & 2 \\
+ -\frac{7}{3} & -1 & -\frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -1 & \frac{8}{9} & \frac{28}{3} \\
+ \frac{34}{9} & \frac{22}{9} & \fbox{$-\frac{14}{3}$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{1}{3} & -2 \\
+ -\frac{4}{3} & -\frac{4}{3} & -\frac{2}{3} \\
+ -\frac{4}{3} & \frac{2}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{8}{3} & -\frac{2}{3} & \frac{8}{3} \\
+ 1 & -\frac{2}{3} & 2 \\
+ -\frac{7}{3} & -1 & -\frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -1 & \frac{8}{9} & \frac{28}{3} \\
+ \frac{34}{9} & \frac{22}{9} & -\frac{14}{3} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{4}{3}\right)\, \left(-\frac{8}{3}\right)+\frac{2}{3}-\frac{7}{3\ 3}=\frac{31}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{1}{3} & -2 \\
+ -\frac{4}{3} & -\frac{4}{3} & -\frac{2}{3} \\
+ -\frac{4}{3} & \frac{2}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{8}{3} & -\frac{2}{3} & \frac{8}{3} \\
+ 1 & -\frac{2}{3} & 2 \\
+ -\frac{7}{3} & -1 & -\frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -1 & \frac{8}{9} & \frac{28}{3} \\
+ \frac{34}{9} & \frac{22}{9} & -\frac{14}{3} \\
+ \fbox{$\frac{31}{9}$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{1}{3} & -2 \\
+ -\frac{4}{3} & -\frac{4}{3} & -\frac{2}{3} \\
+ -\frac{4}{3} & \frac{2}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{8}{3} & -\frac{2}{3} & \frac{8}{3} \\
+ 1 & -\frac{2}{3} & 2 \\
+ -\frac{7}{3} & -1 & -\frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -1 & \frac{8}{9} & \frac{28}{3} \\
+ \frac{34}{9} & \frac{22}{9} & -\frac{14}{3} \\
+ \frac{31}{9} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{4}{3}\right)\, \left(-\frac{2}{3}\right)+\frac{2 (-2)}{3\ 3}-\frac{1}{3}=\frac{1}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{1}{3} & -2 \\
+ -\frac{4}{3} & -\frac{4}{3} & -\frac{2}{3} \\
+ -\frac{4}{3} & \frac{2}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{8}{3} & -\frac{2}{3} & \frac{8}{3} \\
+ 1 & -\frac{2}{3} & 2 \\
+ -\frac{7}{3} & -1 & -\frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -1 & \frac{8}{9} & \frac{28}{3} \\
+ \frac{34}{9} & \frac{22}{9} & -\frac{14}{3} \\
+ \frac{31}{9} & \fbox{$\frac{1}{9}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{1}{3} & -2 \\
+ -\frac{4}{3} & -\frac{4}{3} & -\frac{2}{3} \\
+ -\frac{4}{3} & \frac{2}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{8}{3} & -\frac{2}{3} & \frac{8}{3} \\
+ 1 & -\frac{2}{3} & 2 \\
+ -\frac{7}{3} & -1 & -\frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -1 & \frac{8}{9} & \frac{28}{3} \\
+ \frac{34}{9} & \frac{22}{9} & -\frac{14}{3} \\
+ \frac{31}{9} & \frac{1}{9} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{4}{3}\right)\, \times \, \frac{8}{3}+\frac{2\ 2}{3}-\frac{7}{3\ 3}=-3. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ 2 & -\frac{1}{3} & -2 \\
+ -\frac{4}{3} & -\frac{4}{3} & -\frac{2}{3} \\
+ -\frac{4}{3} & \frac{2}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{8}{3} & -\frac{2}{3} & \frac{8}{3} \\
+ 1 & -\frac{2}{3} & 2 \\
+ -\frac{7}{3} & -1 & -\frac{7}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -1 & \frac{8}{9} & \frac{28}{3} \\
+ \frac{34}{9} & \frac{22}{9} & -\frac{14}{3} \\
+ \frac{31}{9} & \frac{1}{9} & \fbox{$-3$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/4104.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/4104.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b54ac7352c5849a28f588cd06364826727c019f1
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/4104.txt
@@ -0,0 +1,222 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ 2 & -3 \\
+ -1 & -2 \\
+ 3 & 2 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -2 \\
+ -1 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ 2 & -3 \\
+ -1 & -2 \\
+ 3 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -2 \\
+ -1 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & -3 \\
+ -1 & -2 \\
+ 3 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -2 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & -3 \\
+ -1 & -2 \\
+ 3 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -2 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2 (-2)+(-3)\, (-1)=-1. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & -3 \\
+ -1 & -2 \\
+ 3 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -2 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$-1$} \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & -3 \\
+ -1 & -2 \\
+ 3 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -2 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ -1 \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, (-2)+(-2)\, (-1)=4. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & -3 \\
+ -1 & -2 \\
+ 3 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -2 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ -1 \\
+ \fbox{$4$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & -3 \\
+ -1 & -2 \\
+ 3 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -2 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ -1 \\
+ 4 \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }3 (-2)+2 (-1)=-8. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ 2 & -3 \\
+ -1 & -2 \\
+ 3 & 2 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -2 \\
+ -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ -1 \\
+ 4 \\
+ \fbox{$-8$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/4302.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/4302.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ede291e59c2988cbe4bb8b84cec1eedfffa3ef28
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/4302.txt
@@ -0,0 +1,231 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ -\frac{17}{8} & \frac{19}{8} & -\frac{43}{16} \\
+ -\frac{13}{8} & -\frac{19}{8} & \frac{11}{4} \\
+ \frac{31}{16} & \frac{21}{8} & \frac{17}{8} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ \frac{9}{8} \\
+ -\frac{23}{8} \\
+ -3 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{17}{8} & \frac{19}{8} & -\frac{43}{16} \\
+ -\frac{13}{8} & -\frac{19}{8} & \frac{11}{4} \\
+ \frac{31}{16} & \frac{21}{8} & \frac{17}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{9}{8} \\
+ -\frac{23}{8} \\
+ -3 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{17}{8} & \frac{19}{8} & -\frac{43}{16} \\
+ -\frac{13}{8} & -\frac{19}{8} & \frac{11}{4} \\
+ \frac{31}{16} & \frac{21}{8} & \frac{17}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{9}{8} \\
+ -\frac{23}{8} \\
+ -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{17}{8} & \frac{19}{8} & -\frac{43}{16} \\
+ -\frac{13}{8} & -\frac{19}{8} & \frac{11}{4} \\
+ \frac{31}{16} & \frac{21}{8} & \frac{17}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{9}{8} \\
+ -\frac{23}{8} \\
+ -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{17}{8}\right)\, \times \, \frac{9}{8}+\frac{19 (-23)}{8\ 8}+\left(-\frac{43}{16}\right)\, (-3)=-\frac{37}{32}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{17}{8} & \frac{19}{8} & -\frac{43}{16} \\
+ -\frac{13}{8} & -\frac{19}{8} & \frac{11}{4} \\
+ \frac{31}{16} & \frac{21}{8} & \frac{17}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{9}{8} \\
+ -\frac{23}{8} \\
+ -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$-\frac{37}{32}$} \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{17}{8} & \frac{19}{8} & -\frac{43}{16} \\
+ -\frac{13}{8} & -\frac{19}{8} & \frac{11}{4} \\
+ \frac{31}{16} & \frac{21}{8} & \frac{17}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{9}{8} \\
+ -\frac{23}{8} \\
+ -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ -\frac{37}{32} \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{13}{8}\right)\, \times \, \frac{9}{8}+\left(-\frac{19}{8}\right)\, \left(-\frac{23}{8}\right)+\frac{11 (-3)}{4}=-\frac{13}{4}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{17}{8} & \frac{19}{8} & -\frac{43}{16} \\
+ -\frac{13}{8} & -\frac{19}{8} & \frac{11}{4} \\
+ \frac{31}{16} & \frac{21}{8} & \frac{17}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{9}{8} \\
+ -\frac{23}{8} \\
+ -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ -\frac{37}{32} \\
+ \fbox{$-\frac{13}{4}$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{17}{8} & \frac{19}{8} & -\frac{43}{16} \\
+ -\frac{13}{8} & -\frac{19}{8} & \frac{11}{4} \\
+ \frac{31}{16} & \frac{21}{8} & \frac{17}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{9}{8} \\
+ -\frac{23}{8} \\
+ -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ -\frac{37}{32} \\
+ -\frac{13}{4} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{31\ 9}{16\ 8}+\frac{21 (-23)}{8\ 8}+\frac{17 (-3)}{8}=-\frac{1503}{128}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ -\frac{17}{8} & \frac{19}{8} & -\frac{43}{16} \\
+ -\frac{13}{8} & -\frac{19}{8} & \frac{11}{4} \\
+ \frac{31}{16} & \frac{21}{8} & \frac{17}{8} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{9}{8} \\
+ -\frac{23}{8} \\
+ -3 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ -\frac{37}{32} \\
+ -\frac{13}{4} \\
+ \fbox{$-\frac{1503}{128}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/44.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/44.txt
new file mode 100644
index 0000000000000000000000000000000000000000..624c459c94ed26eead17077b897c30f25fa5437e
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/44.txt
@@ -0,0 +1,390 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ 2 & -\frac{4}{3} & \frac{1}{3} \\
+ \frac{7}{3} & -3 & -1 \\
+ -\frac{2}{3} & \frac{8}{3} & \frac{1}{3} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{cc}
+ 1 & -\frac{2}{3} \\
+ -\frac{7}{3} & -\frac{1}{3} \\
+ -\frac{8}{3} & 1 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{4}{3} & \frac{1}{3} \\
+ \frac{7}{3} & -3 & -1 \\
+ -\frac{2}{3} & \frac{8}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -\frac{2}{3} \\
+ -\frac{7}{3} & -\frac{1}{3} \\
+ -\frac{8}{3} & 1 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 2. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 2: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{4}{3} & \frac{1}{3} \\
+ \frac{7}{3} & -3 & -1 \\
+ -\frac{2}{3} & \frac{8}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -\frac{2}{3} \\
+ -\frac{7}{3} & -\frac{1}{3} \\
+ -\frac{8}{3} & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{4}{3} & \frac{1}{3} \\
+ \frac{7}{3} & -3 & -1 \\
+ -\frac{2}{3} & \frac{8}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -\frac{2}{3} \\
+ -\frac{7}{3} & -\frac{1}{3} \\
+ -\frac{8}{3} & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2\ 1+\left(-\frac{4}{3}\right)\, \left(-\frac{7}{3}\right)-\frac{8}{3\ 3}=\frac{38}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{4}{3} & \frac{1}{3} \\
+ \frac{7}{3} & -3 & -1 \\
+ -\frac{2}{3} & \frac{8}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -\frac{2}{3} \\
+ -\frac{7}{3} & -\frac{1}{3} \\
+ -\frac{8}{3} & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \fbox{$\frac{38}{9}$} & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{4}{3} & \frac{1}{3} \\
+ \frac{7}{3} & -3 & -1 \\
+ -\frac{2}{3} & \frac{8}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -\frac{2}{3} \\
+ -\frac{7}{3} & -\frac{1}{3} \\
+ -\frac{8}{3} & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{38}{9} & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2 (-2)}{3}+\frac{4}{3\ 3}+\frac{1}{3}=-\frac{5}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{4}{3} & \frac{1}{3} \\
+ \frac{7}{3} & -3 & -1 \\
+ -\frac{2}{3} & \frac{8}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -\frac{2}{3} \\
+ -\frac{7}{3} & -\frac{1}{3} \\
+ -\frac{8}{3} & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{38}{9} & \fbox{$-\frac{5}{9}$} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{4}{3} & \frac{1}{3} \\
+ \frac{7}{3} & -3 & -1 \\
+ -\frac{2}{3} & \frac{8}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -\frac{2}{3} \\
+ -\frac{7}{3} & -\frac{1}{3} \\
+ -\frac{8}{3} & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{38}{9} & -\frac{5}{9} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{7}{3}+(-3)\, \left(-\frac{7}{3}\right)+(-1)\, \left(-\frac{8}{3}\right)=12. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{4}{3} & \frac{1}{3} \\
+ \frac{7}{3} & -3 & -1 \\
+ -\frac{2}{3} & \frac{8}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -\frac{2}{3} \\
+ -\frac{7}{3} & -\frac{1}{3} \\
+ -\frac{8}{3} & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{38}{9} & -\frac{5}{9} \\
+ \fbox{$12$} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{4}{3} & \frac{1}{3} \\
+ \frac{7}{3} & -3 & -1 \\
+ -\frac{2}{3} & \frac{8}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -\frac{2}{3} \\
+ -\frac{7}{3} & -\frac{1}{3} \\
+ -\frac{8}{3} & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{38}{9} & -\frac{5}{9} \\
+ 12 & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{7 (-2)}{3\ 3}+\frac{3}{3}+(-1)\, \times \, 1=-\frac{14}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{4}{3} & \frac{1}{3} \\
+ \frac{7}{3} & -3 & -1 \\
+ -\frac{2}{3} & \frac{8}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -\frac{2}{3} \\
+ -\frac{7}{3} & -\frac{1}{3} \\
+ -\frac{8}{3} & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{38}{9} & -\frac{5}{9} \\
+ 12 & \fbox{$-\frac{14}{9}$} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{4}{3} & \frac{1}{3} \\
+ \frac{7}{3} & -3 & -1 \\
+ -\frac{2}{3} & \frac{8}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -\frac{2}{3} \\
+ -\frac{7}{3} & -\frac{1}{3} \\
+ -\frac{8}{3} & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{38}{9} & -\frac{5}{9} \\
+ 12 & -\frac{14}{9} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{2}{3}\right)\, \times \, 1+\frac{8 (-7)}{3\ 3}-\frac{8}{3\ 3}=-\frac{70}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{4}{3} & \frac{1}{3} \\
+ \frac{7}{3} & -3 & -1 \\
+ -\frac{2}{3} & \frac{8}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -\frac{2}{3} \\
+ -\frac{7}{3} & -\frac{1}{3} \\
+ -\frac{8}{3} & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{38}{9} & -\frac{5}{9} \\
+ 12 & -\frac{14}{9} \\
+ \fbox{$-\frac{70}{9}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 2 & -\frac{4}{3} & \frac{1}{3} \\
+ \frac{7}{3} & -3 & -1 \\
+ -\frac{2}{3} & \frac{8}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -\frac{2}{3} \\
+ -\frac{7}{3} & -\frac{1}{3} \\
+ -\frac{8}{3} & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{38}{9} & -\frac{5}{9} \\
+ 12 & -\frac{14}{9} \\
+ -\frac{70}{9} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{2}{3}\right)\, \left(-\frac{2}{3}\right)+\frac{1}{3} \left(-\frac{8}{3}\right)+\frac{1}{3}=-\frac{1}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ 2 & -\frac{4}{3} & \frac{1}{3} \\
+ \frac{7}{3} & -3 & -1 \\
+ -\frac{2}{3} & \frac{8}{3} & \frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & -\frac{2}{3} \\
+ -\frac{7}{3} & -\frac{1}{3} \\
+ -\frac{8}{3} & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{38}{9} & -\frac{5}{9} \\
+ 12 & -\frac{14}{9} \\
+ -\frac{70}{9} & \fbox{$-\frac{1}{9}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/4405.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/4405.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3c86cb1cb2eaba28b4520e1ae0a7710ffc17a6e2
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/4405.txt
@@ -0,0 +1,362 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ -\frac{9}{8} & \frac{5}{8} & \frac{7}{8} \\
+ \frac{11}{8} & -1 & \frac{11}{4} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ -\frac{3}{8} & \frac{5}{2} & \frac{3}{2} \\
+ -\frac{21}{8} & -\frac{9}{8} & \frac{1}{4} \\
+ \frac{17}{8} & \frac{21}{8} & \frac{7}{8} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{9}{8} & \frac{5}{8} & \frac{7}{8} \\
+ \frac{11}{8} & -1 & \frac{11}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{3}{8} & \frac{5}{2} & \frac{3}{2} \\
+ -\frac{21}{8} & -\frac{9}{8} & \frac{1}{4} \\
+ \frac{17}{8} & \frac{21}{8} & \frac{7}{8} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{9}{8} & \frac{5}{8} & \frac{7}{8} \\
+ \frac{11}{8} & -1 & \frac{11}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{3}{8} & \frac{5}{2} & \frac{3}{2} \\
+ -\frac{21}{8} & -\frac{9}{8} & \frac{1}{4} \\
+ \frac{17}{8} & \frac{21}{8} & \frac{7}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{9}{8} & \frac{5}{8} & \frac{7}{8} \\
+ \frac{11}{8} & -1 & \frac{11}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{3}{8} & \frac{5}{2} & \frac{3}{2} \\
+ -\frac{21}{8} & -\frac{9}{8} & \frac{1}{4} \\
+ \frac{17}{8} & \frac{21}{8} & \frac{7}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{9}{8}\right)\, \left(-\frac{3}{8}\right)+\frac{5 (-21)}{8\ 8}+\frac{7\ 17}{8\ 8}=\frac{41}{64}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{9}{8} & \frac{5}{8} & \frac{7}{8} \\
+ \frac{11}{8} & -1 & \frac{11}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{3}{8} & \frac{5}{2} & \frac{3}{2} \\
+ -\frac{21}{8} & -\frac{9}{8} & \frac{1}{4} \\
+ \frac{17}{8} & \frac{21}{8} & \frac{7}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$\frac{41}{64}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{9}{8} & \frac{5}{8} & \frac{7}{8} \\
+ \frac{11}{8} & -1 & \frac{11}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{3}{8} & \frac{5}{2} & \frac{3}{2} \\
+ -\frac{21}{8} & -\frac{9}{8} & \frac{1}{4} \\
+ \frac{17}{8} & \frac{21}{8} & \frac{7}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{41}{64} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{9}{8}\right)\, \times \, \frac{5}{2}+\frac{5 (-9)}{8\ 8}+\frac{7\ 21}{8\ 8}=-\frac{39}{32}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{9}{8} & \frac{5}{8} & \frac{7}{8} \\
+ \frac{11}{8} & -1 & \frac{11}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{3}{8} & \frac{5}{2} & \frac{3}{2} \\
+ -\frac{21}{8} & -\frac{9}{8} & \frac{1}{4} \\
+ \frac{17}{8} & \frac{21}{8} & \frac{7}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{41}{64} & \fbox{$-\frac{39}{32}$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{9}{8} & \frac{5}{8} & \frac{7}{8} \\
+ \frac{11}{8} & -1 & \frac{11}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{3}{8} & \frac{5}{2} & \frac{3}{2} \\
+ -\frac{21}{8} & -\frac{9}{8} & \frac{1}{4} \\
+ \frac{17}{8} & \frac{21}{8} & \frac{7}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{41}{64} & -\frac{39}{32} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{9}{8}\right)\, \times \, \frac{3}{2}+\frac{5}{8\ 4}+\frac{7\ 7}{8\ 8}=-\frac{49}{64}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{9}{8} & \frac{5}{8} & \frac{7}{8} \\
+ \frac{11}{8} & -1 & \frac{11}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{3}{8} & \frac{5}{2} & \frac{3}{2} \\
+ -\frac{21}{8} & -\frac{9}{8} & \frac{1}{4} \\
+ \frac{17}{8} & \frac{21}{8} & \frac{7}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{41}{64} & -\frac{39}{32} & \fbox{$-\frac{49}{64}$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{9}{8} & \frac{5}{8} & \frac{7}{8} \\
+ \frac{11}{8} & -1 & \frac{11}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{3}{8} & \frac{5}{2} & \frac{3}{2} \\
+ -\frac{21}{8} & -\frac{9}{8} & \frac{1}{4} \\
+ \frac{17}{8} & \frac{21}{8} & \frac{7}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{41}{64} & -\frac{39}{32} & -\frac{49}{64} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{11 (-3)}{8\ 8}+(-1)\, \left(-\frac{21}{8}\right)+\frac{11\ 17}{4\ 8}=\frac{509}{64}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{9}{8} & \frac{5}{8} & \frac{7}{8} \\
+ \frac{11}{8} & -1 & \frac{11}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{3}{8} & \frac{5}{2} & \frac{3}{2} \\
+ -\frac{21}{8} & -\frac{9}{8} & \frac{1}{4} \\
+ \frac{17}{8} & \frac{21}{8} & \frac{7}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{41}{64} & -\frac{39}{32} & -\frac{49}{64} \\
+ \fbox{$\frac{509}{64}$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{9}{8} & \frac{5}{8} & \frac{7}{8} \\
+ \frac{11}{8} & -1 & \frac{11}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{3}{8} & \frac{5}{2} & \frac{3}{2} \\
+ -\frac{21}{8} & -\frac{9}{8} & \frac{1}{4} \\
+ \frac{17}{8} & \frac{21}{8} & \frac{7}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{41}{64} & -\frac{39}{32} & -\frac{49}{64} \\
+ \frac{509}{64} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{11\ 5}{8\ 2}+(-1)\, \left(-\frac{9}{8}\right)+\frac{11\ 21}{4\ 8}=\frac{377}{32}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{9}{8} & \frac{5}{8} & \frac{7}{8} \\
+ \frac{11}{8} & -1 & \frac{11}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{3}{8} & \frac{5}{2} & \frac{3}{2} \\
+ -\frac{21}{8} & -\frac{9}{8} & \frac{1}{4} \\
+ \frac{17}{8} & \frac{21}{8} & \frac{7}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{41}{64} & -\frac{39}{32} & -\frac{49}{64} \\
+ \frac{509}{64} & \fbox{$\frac{377}{32}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{9}{8} & \frac{5}{8} & \frac{7}{8} \\
+ \frac{11}{8} & -1 & \frac{11}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{3}{8} & \frac{5}{2} & \frac{3}{2} \\
+ -\frac{21}{8} & -\frac{9}{8} & \frac{1}{4} \\
+ \frac{17}{8} & \frac{21}{8} & \frac{7}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{41}{64} & -\frac{39}{32} & -\frac{49}{64} \\
+ \frac{509}{64} & \frac{377}{32} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{11\ 3}{8\ 2}+(-1)\, \times \, \frac{1}{4}+\frac{11\ 7}{4\ 8}=\frac{135}{32}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ -\frac{9}{8} & \frac{5}{8} & \frac{7}{8} \\
+ \frac{11}{8} & -1 & \frac{11}{4} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{3}{8} & \frac{5}{2} & \frac{3}{2} \\
+ -\frac{21}{8} & -\frac{9}{8} & \frac{1}{4} \\
+ \frac{17}{8} & \frac{21}{8} & \frac{7}{8} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{41}{64} & -\frac{39}{32} & -\frac{49}{64} \\
+ \frac{509}{64} & \frac{377}{32} & \fbox{$\frac{135}{32}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/4516.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/4516.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e7bdba51a6ce5c5724ffe7f219612f430382dc84
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/4516.txt
@@ -0,0 +1,375 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ 2 & -2 \\
+ -3 & 1 \\
+ -2 & 0 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{cc}
+ 0 & 2 \\
+ -1 & 1 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ 2 & -2 \\
+ -3 & 1 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & 2 \\
+ -1 & 1 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 2. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 2: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & -2 \\
+ -3 & 1 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & 2 \\
+ -1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & -2 \\
+ -3 & 1 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & 2 \\
+ -1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2\ 0+(-2)\, (-1)=2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & -2 \\
+ -3 & 1 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & 2 \\
+ -1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \fbox{$2$} & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & -2 \\
+ -3 & 1 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & 2 \\
+ -1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 2 & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2\ 2+(-2)\, \times \, 1=2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & -2 \\
+ -3 & 1 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & 2 \\
+ -1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 2 & \fbox{$2$} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & -2 \\
+ -3 & 1 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & 2 \\
+ -1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 2 & 2 \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-3)\, \times \, 0+1 (-1)=-1. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & -2 \\
+ -3 & 1 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & 2 \\
+ -1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 2 & 2 \\
+ \fbox{$-1$} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & -2 \\
+ -3 & 1 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & 2 \\
+ -1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 2 & 2 \\
+ -1 & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-3)\, \times \, 2+1\ 1=-5. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & -2 \\
+ -3 & 1 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & 2 \\
+ -1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 2 & 2 \\
+ -1 & \fbox{$-5$} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & -2 \\
+ -3 & 1 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & 2 \\
+ -1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 2 & 2 \\
+ -1 & -5 \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, \times \, 0+0 (-1)=0. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & -2 \\
+ -3 & 1 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & 2 \\
+ -1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 2 & 2 \\
+ -1 & -5 \\
+ \fbox{$0$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & -2 \\
+ -3 & 1 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & 2 \\
+ -1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 2 & 2 \\
+ -1 & -5 \\
+ 0 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, \times \, 2+0\ 1=-4. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ 2 & -2 \\
+ -3 & 1 \\
+ -2 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 0 & 2 \\
+ -1 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 2 & 2 \\
+ -1 & -5 \\
+ 0 & \fbox{$-4$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/461.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/461.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c4bec1d20bef7b711391158f77b13e304412e45d
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/461.txt
@@ -0,0 +1,528 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ -3 & 2 \\
+ 3 & 0 \\
+ -1 & 1 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ 1 & -1 & 2 \\
+ 2 & 0 & -2 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ -3 & 2 \\
+ 3 & 0 \\
+ -1 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -1 & 2 \\
+ 2 & 0 & -2 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -3 & 2 \\
+ 3 & 0 \\
+ -1 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -1 & 2 \\
+ 2 & 0 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -3 & 2 \\
+ 3 & 0 \\
+ -1 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -1 & 2 \\
+ 2 & 0 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-3)\, \times \, 1+2\ 2=1. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -3 & 2 \\
+ 3 & 0 \\
+ -1 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -1 & 2 \\
+ 2 & 0 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$1$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -3 & 2 \\
+ 3 & 0 \\
+ -1 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -1 & 2 \\
+ 2 & 0 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 1 & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-3)\, (-1)+2\ 0=3. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -3 & 2 \\
+ 3 & 0 \\
+ -1 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -1 & 2 \\
+ 2 & 0 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 1 & \fbox{$3$} & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -3 & 2 \\
+ 3 & 0 \\
+ -1 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -1 & 2 \\
+ 2 & 0 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 1 & 3 & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-3)\, \times \, 2+2 (-2)=-10. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -3 & 2 \\
+ 3 & 0 \\
+ -1 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -1 & 2 \\
+ 2 & 0 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 1 & 3 & \fbox{$-10$} \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -3 & 2 \\
+ 3 & 0 \\
+ -1 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -1 & 2 \\
+ 2 & 0 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 1 & 3 & -10 \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }3\ 1+0\ 2=3. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -3 & 2 \\
+ 3 & 0 \\
+ -1 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -1 & 2 \\
+ 2 & 0 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 1 & 3 & -10 \\
+ \fbox{$3$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -3 & 2 \\
+ 3 & 0 \\
+ -1 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -1 & 2 \\
+ 2 & 0 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 1 & 3 & -10 \\
+ 3 & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }3 (-1)+0\ 0=-3. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -3 & 2 \\
+ 3 & 0 \\
+ -1 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -1 & 2 \\
+ 2 & 0 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 1 & 3 & -10 \\
+ 3 & \fbox{$-3$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -3 & 2 \\
+ 3 & 0 \\
+ -1 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -1 & 2 \\
+ 2 & 0 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 1 & 3 & -10 \\
+ 3 & -3 & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }3\ 2+0 (-2)=6. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -3 & 2 \\
+ 3 & 0 \\
+ -1 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -1 & 2 \\
+ 2 & 0 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 1 & 3 & -10 \\
+ 3 & -3 & \fbox{$6$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -3 & 2 \\
+ 3 & 0 \\
+ -1 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -1 & 2 \\
+ 2 & 0 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 1 & 3 & -10 \\
+ 3 & -3 & 6 \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, \times \, 1+1\ 2=1. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -3 & 2 \\
+ 3 & 0 \\
+ -1 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -1 & 2 \\
+ 2 & 0 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 1 & 3 & -10 \\
+ 3 & -3 & 6 \\
+ \fbox{$1$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -3 & 2 \\
+ 3 & 0 \\
+ -1 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -1 & 2 \\
+ 2 & 0 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 1 & 3 & -10 \\
+ 3 & -3 & 6 \\
+ 1 & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, (-1)+1\ 0=1. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -3 & 2 \\
+ 3 & 0 \\
+ -1 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -1 & 2 \\
+ 2 & 0 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 1 & 3 & -10 \\
+ 3 & -3 & 6 \\
+ 1 & \fbox{$1$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -3 & 2 \\
+ 3 & 0 \\
+ -1 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -1 & 2 \\
+ 2 & 0 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 1 & 3 & -10 \\
+ 3 & -3 & 6 \\
+ 1 & 1 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, \times \, 2+1 (-2)=-4. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ -3 & 2 \\
+ 3 & 0 \\
+ -1 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 1 & -1 & 2 \\
+ 2 & 0 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 1 & 3 & -10 \\
+ 3 & -3 & 6 \\
+ 1 & 1 & \fbox{$-4$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/4640.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/4640.txt
new file mode 100644
index 0000000000000000000000000000000000000000..02b710384a17bd792ee8fbce5927b38915f47cc1
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/4640.txt
@@ -0,0 +1,375 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ 1 & 3 \\
+ 0 & 2 \\
+ 0 & -2 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ -1 & 0 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ 1 & 3 \\
+ 0 & 2 \\
+ 0 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ -1 & 0 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 2. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 2: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 1 & 3 \\
+ 0 & 2 \\
+ 0 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ -1 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 1 & 3 \\
+ 0 & 2 \\
+ 0 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ -1 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1\ 1+3 (-1)=-2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 1 & 3 \\
+ 0 & 2 \\
+ 0 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ -1 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \fbox{$-2$} & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 1 & 3 \\
+ 0 & 2 \\
+ 0 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ -1 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -2 & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1\ 0+3\ 0=0. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 1 & 3 \\
+ 0 & 2 \\
+ 0 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ -1 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -2 & \fbox{$0$} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 1 & 3 \\
+ 0 & 2 \\
+ 0 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ -1 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -2 & 0 \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0\ 1+2 (-1)=-2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 1 & 3 \\
+ 0 & 2 \\
+ 0 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ -1 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -2 & 0 \\
+ \fbox{$-2$} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 1 & 3 \\
+ 0 & 2 \\
+ 0 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ -1 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -2 & 0 \\
+ -2 & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0\ 0+2\ 0=0. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 1 & 3 \\
+ 0 & 2 \\
+ 0 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ -1 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -2 & 0 \\
+ -2 & \fbox{$0$} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 1 & 3 \\
+ 0 & 2 \\
+ 0 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ -1 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -2 & 0 \\
+ -2 & 0 \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0\ 1+(-2)\, (-1)=2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 1 & 3 \\
+ 0 & 2 \\
+ 0 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ -1 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -2 & 0 \\
+ -2 & 0 \\
+ \fbox{$2$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 1 & 3 \\
+ 0 & 2 \\
+ 0 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ -1 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -2 & 0 \\
+ -2 & 0 \\
+ 2 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0\ 0+(-2)\, \times \, 0=0. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ 1 & 3 \\
+ 0 & 2 \\
+ 0 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ -1 & 0 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ -2 & 0 \\
+ -2 & 0 \\
+ 2 & \fbox{$0$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/4655.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/4655.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fea4add394ba9fe3681e7138365d04e9839a2802
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/4655.txt
@@ -0,0 +1,375 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ -2 & 2 \\
+ 2 & 2 \\
+ 2 & 1 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ 1 & 2 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ -2 & 2 \\
+ 2 & 2 \\
+ 2 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ 1 & 2 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 2. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 2: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -2 & 2 \\
+ 2 & 2 \\
+ 2 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -2 & 2 \\
+ 2 & 2 \\
+ 2 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, (-1)+2\ 1=4. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -2 & 2 \\
+ 2 & 2 \\
+ 2 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \fbox{$4$} & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -2 & 2 \\
+ 2 & 2 \\
+ 2 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, \times \, 3+2\ 2=-2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -2 & 2 \\
+ 2 & 2 \\
+ 2 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & \fbox{$-2$} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -2 & 2 \\
+ 2 & 2 \\
+ 2 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & -2 \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2 (-1)+2\ 1=0. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -2 & 2 \\
+ 2 & 2 \\
+ 2 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & -2 \\
+ \fbox{$0$} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -2 & 2 \\
+ 2 & 2 \\
+ 2 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & -2 \\
+ 0 & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2\ 3+2\ 2=10. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -2 & 2 \\
+ 2 & 2 \\
+ 2 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & -2 \\
+ 0 & \fbox{$10$} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -2 & 2 \\
+ 2 & 2 \\
+ 2 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & -2 \\
+ 0 & 10 \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2 (-1)+1\ 1=-1. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -2 & 2 \\
+ 2 & 2 \\
+ 2 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & -2 \\
+ 0 & 10 \\
+ \fbox{$-1$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -2 & 2 \\
+ 2 & 2 \\
+ 2 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & -2 \\
+ 0 & 10 \\
+ -1 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2\ 3+1\ 2=8. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ -2 & 2 \\
+ 2 & 2 \\
+ 2 & 1 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ -1 & 3 \\
+ 1 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 4 & -2 \\
+ 0 & 10 \\
+ -1 & \fbox{$8$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/4683.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/4683.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f2ba4f0579e1457946ebc1cc644d33f5dff2a565
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/4683.txt
@@ -0,0 +1,362 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ -3 & -2 & -2 \\
+ 0 & 1 & 3 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ 0 & -2 & 0 \\
+ -1 & 1 & 2 \\
+ 2 & 2 & -1 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ -3 & -2 & -2 \\
+ 0 & 1 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & -2 & 0 \\
+ -1 & 1 & 2 \\
+ 2 & 2 & -1 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -3 & -2 & -2 \\
+ 0 & 1 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & -2 & 0 \\
+ -1 & 1 & 2 \\
+ 2 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -3 & -2 & -2 \\
+ 0 & 1 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & -2 & 0 \\
+ -1 & 1 & 2 \\
+ 2 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-3)\, \times \, 0+(-2)\, (-1)+(-2)\, \times \, 2=-2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -3 & -2 & -2 \\
+ 0 & 1 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & -2 & 0 \\
+ -1 & 1 & 2 \\
+ 2 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$-2$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -3 & -2 & -2 \\
+ 0 & 1 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & -2 & 0 \\
+ -1 & 1 & 2 \\
+ 2 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -2 & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-3)\, (-2)+(-2)\, \times \, 1+(-2)\, \times \, 2=0. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -3 & -2 & -2 \\
+ 0 & 1 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & -2 & 0 \\
+ -1 & 1 & 2 \\
+ 2 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -2 & \fbox{$0$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -3 & -2 & -2 \\
+ 0 & 1 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & -2 & 0 \\
+ -1 & 1 & 2 \\
+ 2 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -2 & 0 & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-3)\, \times \, 0+(-2)\, \times \, 2+(-2)\, (-1)=-2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -3 & -2 & -2 \\
+ 0 & 1 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & -2 & 0 \\
+ -1 & 1 & 2 \\
+ 2 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -2 & 0 & \fbox{$-2$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -3 & -2 & -2 \\
+ 0 & 1 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & -2 & 0 \\
+ -1 & 1 & 2 \\
+ 2 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -2 & 0 & -2 \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0\ 0+1 (-1)+3\ 2=5. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -3 & -2 & -2 \\
+ 0 & 1 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & -2 & 0 \\
+ -1 & 1 & 2 \\
+ 2 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -2 & 0 & -2 \\
+ \fbox{$5$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -3 & -2 & -2 \\
+ 0 & 1 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & -2 & 0 \\
+ -1 & 1 & 2 \\
+ 2 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -2 & 0 & -2 \\
+ 5 & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0 (-2)+1\ 1+3\ 2=7. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -3 & -2 & -2 \\
+ 0 & 1 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & -2 & 0 \\
+ -1 & 1 & 2 \\
+ 2 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -2 & 0 & -2 \\
+ 5 & \fbox{$7$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -3 & -2 & -2 \\
+ 0 & 1 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & -2 & 0 \\
+ -1 & 1 & 2 \\
+ 2 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -2 & 0 & -2 \\
+ 5 & 7 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0\ 0+1\ 2+3 (-1)=-1. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ -3 & -2 & -2 \\
+ 0 & 1 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 0 & -2 & 0 \\
+ -1 & 1 & 2 \\
+ 2 & 2 & -1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -2 & 0 & -2 \\
+ 5 & 7 & \fbox{$-1$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/4715.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/4715.txt
new file mode 100644
index 0000000000000000000000000000000000000000..96e2eed442206de51f45dc6c31836a22f1ea1189
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/4715.txt
@@ -0,0 +1,549 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ -1 & \frac{5}{3} & 0 \\
+ \frac{4}{3} & \frac{4}{3} & -\frac{5}{3} \\
+ 2 & \frac{5}{3} & -\frac{1}{3} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ \frac{7}{3} & 1 & -\frac{4}{3} \\
+ 1 & -\frac{8}{3} & 1 \\
+ -1 & 2 & -\frac{5}{3} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ -1 & \frac{5}{3} & 0 \\
+ \frac{4}{3} & \frac{4}{3} & -\frac{5}{3} \\
+ 2 & \frac{5}{3} & -\frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{7}{3} & 1 & -\frac{4}{3} \\
+ 1 & -\frac{8}{3} & 1 \\
+ -1 & 2 & -\frac{5}{3} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -1 & \frac{5}{3} & 0 \\
+ \frac{4}{3} & \frac{4}{3} & -\frac{5}{3} \\
+ 2 & \frac{5}{3} & -\frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{7}{3} & 1 & -\frac{4}{3} \\
+ 1 & -\frac{8}{3} & 1 \\
+ -1 & 2 & -\frac{5}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -1 & \frac{5}{3} & 0 \\
+ \frac{4}{3} & \frac{4}{3} & -\frac{5}{3} \\
+ 2 & \frac{5}{3} & -\frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{7}{3} & 1 & -\frac{4}{3} \\
+ 1 & -\frac{8}{3} & 1 \\
+ -1 & 2 & -\frac{5}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, \times \, \frac{7}{3}+\frac{5}{3}+0 (-1)=-\frac{2}{3}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -1 & \frac{5}{3} & 0 \\
+ \frac{4}{3} & \frac{4}{3} & -\frac{5}{3} \\
+ 2 & \frac{5}{3} & -\frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{7}{3} & 1 & -\frac{4}{3} \\
+ 1 & -\frac{8}{3} & 1 \\
+ -1 & 2 & -\frac{5}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$-\frac{2}{3}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -1 & \frac{5}{3} & 0 \\
+ \frac{4}{3} & \frac{4}{3} & -\frac{5}{3} \\
+ 2 & \frac{5}{3} & -\frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{7}{3} & 1 & -\frac{4}{3} \\
+ 1 & -\frac{8}{3} & 1 \\
+ -1 & 2 & -\frac{5}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{2}{3} & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, \times \, 1+\frac{5 (-8)}{3\ 3}+0\ 2=-\frac{49}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -1 & \frac{5}{3} & 0 \\
+ \frac{4}{3} & \frac{4}{3} & -\frac{5}{3} \\
+ 2 & \frac{5}{3} & -\frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{7}{3} & 1 & -\frac{4}{3} \\
+ 1 & -\frac{8}{3} & 1 \\
+ -1 & 2 & -\frac{5}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{2}{3} & \fbox{$-\frac{49}{9}$} & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -1 & \frac{5}{3} & 0 \\
+ \frac{4}{3} & \frac{4}{3} & -\frac{5}{3} \\
+ 2 & \frac{5}{3} & -\frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{7}{3} & 1 & -\frac{4}{3} \\
+ 1 & -\frac{8}{3} & 1 \\
+ -1 & 2 & -\frac{5}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{2}{3} & -\frac{49}{9} & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, \left(-\frac{4}{3}\right)+\frac{5}{3}+\frac{0 (-5)}{3}=3. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -1 & \frac{5}{3} & 0 \\
+ \frac{4}{3} & \frac{4}{3} & -\frac{5}{3} \\
+ 2 & \frac{5}{3} & -\frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{7}{3} & 1 & -\frac{4}{3} \\
+ 1 & -\frac{8}{3} & 1 \\
+ -1 & 2 & -\frac{5}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{2}{3} & -\frac{49}{9} & \fbox{$3$} \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -1 & \frac{5}{3} & 0 \\
+ \frac{4}{3} & \frac{4}{3} & -\frac{5}{3} \\
+ 2 & \frac{5}{3} & -\frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{7}{3} & 1 & -\frac{4}{3} \\
+ 1 & -\frac{8}{3} & 1 \\
+ -1 & 2 & -\frac{5}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{2}{3} & -\frac{49}{9} & 3 \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{4\ 7}{3\ 3}+\frac{4}{3}+\left(-\frac{5}{3}\right)\, (-1)=\frac{55}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -1 & \frac{5}{3} & 0 \\
+ \frac{4}{3} & \frac{4}{3} & -\frac{5}{3} \\
+ 2 & \frac{5}{3} & -\frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{7}{3} & 1 & -\frac{4}{3} \\
+ 1 & -\frac{8}{3} & 1 \\
+ -1 & 2 & -\frac{5}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{2}{3} & -\frac{49}{9} & 3 \\
+ \fbox{$\frac{55}{9}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -1 & \frac{5}{3} & 0 \\
+ \frac{4}{3} & \frac{4}{3} & -\frac{5}{3} \\
+ 2 & \frac{5}{3} & -\frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{7}{3} & 1 & -\frac{4}{3} \\
+ 1 & -\frac{8}{3} & 1 \\
+ -1 & 2 & -\frac{5}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{2}{3} & -\frac{49}{9} & 3 \\
+ \frac{55}{9} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{4}{3}+\frac{4 (-8)}{3\ 3}+\left(-\frac{5}{3}\right)\, \times \, 2=-\frac{50}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -1 & \frac{5}{3} & 0 \\
+ \frac{4}{3} & \frac{4}{3} & -\frac{5}{3} \\
+ 2 & \frac{5}{3} & -\frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{7}{3} & 1 & -\frac{4}{3} \\
+ 1 & -\frac{8}{3} & 1 \\
+ -1 & 2 & -\frac{5}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{2}{3} & -\frac{49}{9} & 3 \\
+ \frac{55}{9} & \fbox{$-\frac{50}{9}$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -1 & \frac{5}{3} & 0 \\
+ \frac{4}{3} & \frac{4}{3} & -\frac{5}{3} \\
+ 2 & \frac{5}{3} & -\frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{7}{3} & 1 & -\frac{4}{3} \\
+ 1 & -\frac{8}{3} & 1 \\
+ -1 & 2 & -\frac{5}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{2}{3} & -\frac{49}{9} & 3 \\
+ \frac{55}{9} & -\frac{50}{9} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{4 (-4)}{3\ 3}+\frac{4}{3}+\left(-\frac{5}{3}\right)\, \left(-\frac{5}{3}\right)=\frac{7}{3}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -1 & \frac{5}{3} & 0 \\
+ \frac{4}{3} & \frac{4}{3} & -\frac{5}{3} \\
+ 2 & \frac{5}{3} & -\frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{7}{3} & 1 & -\frac{4}{3} \\
+ 1 & -\frac{8}{3} & 1 \\
+ -1 & 2 & -\frac{5}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{2}{3} & -\frac{49}{9} & 3 \\
+ \frac{55}{9} & -\frac{50}{9} & \fbox{$\frac{7}{3}$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -1 & \frac{5}{3} & 0 \\
+ \frac{4}{3} & \frac{4}{3} & -\frac{5}{3} \\
+ 2 & \frac{5}{3} & -\frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{7}{3} & 1 & -\frac{4}{3} \\
+ 1 & -\frac{8}{3} & 1 \\
+ -1 & 2 & -\frac{5}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{2}{3} & -\frac{49}{9} & 3 \\
+ \frac{55}{9} & -\frac{50}{9} & \frac{7}{3} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2\ 7}{3}+\frac{5}{3}+\frac{1}{3}=\frac{20}{3}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -1 & \frac{5}{3} & 0 \\
+ \frac{4}{3} & \frac{4}{3} & -\frac{5}{3} \\
+ 2 & \frac{5}{3} & -\frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{7}{3} & 1 & -\frac{4}{3} \\
+ 1 & -\frac{8}{3} & 1 \\
+ -1 & 2 & -\frac{5}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{2}{3} & -\frac{49}{9} & 3 \\
+ \frac{55}{9} & -\frac{50}{9} & \frac{7}{3} \\
+ \fbox{$\frac{20}{3}$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -1 & \frac{5}{3} & 0 \\
+ \frac{4}{3} & \frac{4}{3} & -\frac{5}{3} \\
+ 2 & \frac{5}{3} & -\frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{7}{3} & 1 & -\frac{4}{3} \\
+ 1 & -\frac{8}{3} & 1 \\
+ -1 & 2 & -\frac{5}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{2}{3} & -\frac{49}{9} & 3 \\
+ \frac{55}{9} & -\frac{50}{9} & \frac{7}{3} \\
+ \frac{20}{3} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2\ 1+\frac{5 (-8)}{3\ 3}+\frac{1}{3} (-2)=-\frac{28}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -1 & \frac{5}{3} & 0 \\
+ \frac{4}{3} & \frac{4}{3} & -\frac{5}{3} \\
+ 2 & \frac{5}{3} & -\frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{7}{3} & 1 & -\frac{4}{3} \\
+ 1 & -\frac{8}{3} & 1 \\
+ -1 & 2 & -\frac{5}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{2}{3} & -\frac{49}{9} & 3 \\
+ \frac{55}{9} & -\frac{50}{9} & \frac{7}{3} \\
+ \frac{20}{3} & \fbox{$-\frac{28}{9}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -1 & \frac{5}{3} & 0 \\
+ \frac{4}{3} & \frac{4}{3} & -\frac{5}{3} \\
+ 2 & \frac{5}{3} & -\frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{7}{3} & 1 & -\frac{4}{3} \\
+ 1 & -\frac{8}{3} & 1 \\
+ -1 & 2 & -\frac{5}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{2}{3} & -\frac{49}{9} & 3 \\
+ \frac{55}{9} & -\frac{50}{9} & \frac{7}{3} \\
+ \frac{20}{3} & -\frac{28}{9} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2 (-4)}{3}+\frac{5}{3}+\frac{5}{3\ 3}=-\frac{4}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ -1 & \frac{5}{3} & 0 \\
+ \frac{4}{3} & \frac{4}{3} & -\frac{5}{3} \\
+ 2 & \frac{5}{3} & -\frac{1}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ \frac{7}{3} & 1 & -\frac{4}{3} \\
+ 1 & -\frac{8}{3} & 1 \\
+ -1 & 2 & -\frac{5}{3} \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -\frac{2}{3} & -\frac{49}{9} & 3 \\
+ \frac{55}{9} & -\frac{50}{9} & \frac{7}{3} \\
+ \frac{20}{3} & -\frac{28}{9} & \fbox{$-\frac{4}{9}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/4753.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/4753.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cdb353b6692fc6a2eb2ff99baca0afa4d7829b93
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/4753.txt
@@ -0,0 +1,264 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ \frac{6}{5} & \frac{7}{5} & -\frac{1}{5} \\
+ \frac{2}{5} & \frac{3}{5} & -\frac{9}{5} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{4}{5} \\
+ \frac{13}{5} & -\frac{13}{5} \\
+ -\frac{3}{5} & \frac{7}{5} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{6}{5} & \frac{7}{5} & -\frac{1}{5} \\
+ \frac{2}{5} & \frac{3}{5} & -\frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{4}{5} \\
+ \frac{13}{5} & -\frac{13}{5} \\
+ -\frac{3}{5} & \frac{7}{5} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 2. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 2: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{6}{5} & \frac{7}{5} & -\frac{1}{5} \\
+ \frac{2}{5} & \frac{3}{5} & -\frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{4}{5} \\
+ \frac{13}{5} & -\frac{13}{5} \\
+ -\frac{3}{5} & \frac{7}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{6}{5} & \frac{7}{5} & -\frac{1}{5} \\
+ \frac{2}{5} & \frac{3}{5} & -\frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{4}{5} \\
+ \frac{13}{5} & -\frac{13}{5} \\
+ -\frac{3}{5} & \frac{7}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{6\ 3}{5\ 5}+\frac{7\ 13}{5\ 5}+\frac{3}{5\ 5}=\frac{112}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{6}{5} & \frac{7}{5} & -\frac{1}{5} \\
+ \frac{2}{5} & \frac{3}{5} & -\frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{4}{5} \\
+ \frac{13}{5} & -\frac{13}{5} \\
+ -\frac{3}{5} & \frac{7}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \fbox{$\frac{112}{25}$} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{6}{5} & \frac{7}{5} & -\frac{1}{5} \\
+ \frac{2}{5} & \frac{3}{5} & -\frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{4}{5} \\
+ \frac{13}{5} & -\frac{13}{5} \\
+ -\frac{3}{5} & \frac{7}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{112}{25} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{6 (-4)}{5\ 5}+\frac{7 (-13)}{5\ 5}+\frac{1}{5} \left(-\frac{7}{5}\right)=-\frac{122}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{6}{5} & \frac{7}{5} & -\frac{1}{5} \\
+ \frac{2}{5} & \frac{3}{5} & -\frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{4}{5} \\
+ \frac{13}{5} & -\frac{13}{5} \\
+ -\frac{3}{5} & \frac{7}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{112}{25} & \fbox{$-\frac{122}{25}$} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{6}{5} & \frac{7}{5} & -\frac{1}{5} \\
+ \frac{2}{5} & \frac{3}{5} & -\frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{4}{5} \\
+ \frac{13}{5} & -\frac{13}{5} \\
+ -\frac{3}{5} & \frac{7}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{112}{25} & -\frac{122}{25} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2\ 3}{5\ 5}+\frac{3\ 13}{5\ 5}+\left(-\frac{9}{5}\right)\, \left(-\frac{3}{5}\right)=\frac{72}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ \frac{6}{5} & \frac{7}{5} & -\frac{1}{5} \\
+ \frac{2}{5} & \frac{3}{5} & -\frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{4}{5} \\
+ \frac{13}{5} & -\frac{13}{5} \\
+ -\frac{3}{5} & \frac{7}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{112}{25} & -\frac{122}{25} \\
+ \fbox{$\frac{72}{25}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ \frac{6}{5} & \frac{7}{5} & -\frac{1}{5} \\
+ \frac{2}{5} & \frac{3}{5} & -\frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{4}{5} \\
+ \frac{13}{5} & -\frac{13}{5} \\
+ -\frac{3}{5} & \frac{7}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{112}{25} & -\frac{122}{25} \\
+ \frac{72}{25} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{2 (-4)}{5\ 5}+\frac{3 (-13)}{5\ 5}+\left(-\frac{9}{5}\right)\, \times \, \frac{7}{5}=-\frac{22}{5}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ \frac{6}{5} & \frac{7}{5} & -\frac{1}{5} \\
+ \frac{2}{5} & \frac{3}{5} & -\frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{3}{5} & -\frac{4}{5} \\
+ \frac{13}{5} & -\frac{13}{5} \\
+ -\frac{3}{5} & \frac{7}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{112}{25} & -\frac{122}{25} \\
+ \frac{72}{25} & \fbox{$-\frac{22}{5}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/4781.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/4781.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9ceb5dff1678eb62bd05e12e8cbb62e300c22ea6
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/4781.txt
@@ -0,0 +1,253 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ -\frac{1}{5} & \frac{14}{5} \\
+ -\frac{13}{5} & \frac{3}{10} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{cc}
+ \frac{21}{10} & -\frac{7}{10} \\
+ \frac{13}{5} & \frac{12}{5} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{1}{5} & \frac{14}{5} \\
+ -\frac{13}{5} & \frac{3}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{21}{10} & -\frac{7}{10} \\
+ \frac{13}{5} & \frac{12}{5} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 2. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 2: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{1}{5} & \frac{14}{5} \\
+ -\frac{13}{5} & \frac{3}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{21}{10} & -\frac{7}{10} \\
+ \frac{13}{5} & \frac{12}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{1}{5} & \frac{14}{5} \\
+ -\frac{13}{5} & \frac{3}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{21}{10} & -\frac{7}{10} \\
+ \frac{13}{5} & \frac{12}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{1}{5} \left(-\frac{21}{10}\right)+\frac{14\ 13}{5\ 5}=\frac{343}{50}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{1}{5} & \frac{14}{5} \\
+ -\frac{13}{5} & \frac{3}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{21}{10} & -\frac{7}{10} \\
+ \frac{13}{5} & \frac{12}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \fbox{$\frac{343}{50}$} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{1}{5} & \frac{14}{5} \\
+ -\frac{13}{5} & \frac{3}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{21}{10} & -\frac{7}{10} \\
+ \frac{13}{5} & \frac{12}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{343}{50} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{7}{10\ 5}+\frac{14\ 12}{5\ 5}=\frac{343}{50}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{1}{5} & \frac{14}{5} \\
+ -\frac{13}{5} & \frac{3}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{21}{10} & -\frac{7}{10} \\
+ \frac{13}{5} & \frac{12}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{343}{50} & \fbox{$\frac{343}{50}$} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{1}{5} & \frac{14}{5} \\
+ -\frac{13}{5} & \frac{3}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{21}{10} & -\frac{7}{10} \\
+ \frac{13}{5} & \frac{12}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{343}{50} & \frac{343}{50} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{13}{5}\right)\, \times \, \frac{21}{10}+\frac{3\ 13}{10\ 5}=-\frac{117}{25}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{1}{5} & \frac{14}{5} \\
+ -\frac{13}{5} & \frac{3}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{21}{10} & -\frac{7}{10} \\
+ \frac{13}{5} & \frac{12}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{343}{50} & \frac{343}{50} \\
+ \fbox{$-\frac{117}{25}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{1}{5} & \frac{14}{5} \\
+ -\frac{13}{5} & \frac{3}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{21}{10} & -\frac{7}{10} \\
+ \frac{13}{5} & \frac{12}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{343}{50} & \frac{343}{50} \\
+ -\frac{117}{25} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{13}{5}\right)\, \left(-\frac{7}{10}\right)+\frac{3\ 12}{10\ 5}=\frac{127}{50}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ -\frac{1}{5} & \frac{14}{5} \\
+ -\frac{13}{5} & \frac{3}{10} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{21}{10} & -\frac{7}{10} \\
+ \frac{13}{5} & \frac{12}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{343}{50} & \frac{343}{50} \\
+ -\frac{117}{25} & \fbox{$\frac{127}{50}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/4791.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/4791.txt
new file mode 100644
index 0000000000000000000000000000000000000000..defe51b4ced444d863eed42c2c36a09f28c58b96
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/4791.txt
@@ -0,0 +1,159 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ \frac{5}{3} & 1 \\
+ \frac{7}{3} & -\frac{8}{3} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -\frac{7}{3} \\
+ 2 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ \frac{5}{3} & 1 \\
+ \frac{7}{3} & -\frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -\frac{7}{3} \\
+ 2 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{5}{3} & 1 \\
+ \frac{7}{3} & -\frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -\frac{7}{3} \\
+ 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{5}{3} & 1 \\
+ \frac{7}{3} & -\frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -\frac{7}{3} \\
+ 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{5 (-7)}{3\ 3}+1\ 2=-\frac{17}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{5}{3} & 1 \\
+ \frac{7}{3} & -\frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -\frac{7}{3} \\
+ 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$-\frac{17}{9}$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{5}{3} & 1 \\
+ \frac{7}{3} & -\frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -\frac{7}{3} \\
+ 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ -\frac{17}{9} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{7 (-7)}{3\ 3}+\left(-\frac{8}{3}\right)\, \times \, 2=-\frac{97}{9}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ \frac{5}{3} & 1 \\
+ \frac{7}{3} & -\frac{8}{3} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -\frac{7}{3} \\
+ 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ -\frac{17}{9} \\
+ \fbox{$-\frac{97}{9}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/4849.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/4849.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8c7b823b75a29fa0bfe05ae83165931a9b926bd1
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/4849.txt
@@ -0,0 +1,390 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{3}{10} & -\frac{13}{10} \\
+ -\frac{3}{10} & \frac{6}{5} & -\frac{9}{5} \\
+ \frac{13}{10} & -\frac{27}{10} & \frac{13}{5} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{11}{5} \\
+ \frac{29}{10} & \frac{7}{10} \\
+ \frac{1}{5} & \frac{8}{5} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{3}{10} & -\frac{13}{10} \\
+ -\frac{3}{10} & \frac{6}{5} & -\frac{9}{5} \\
+ \frac{13}{10} & -\frac{27}{10} & \frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{11}{5} \\
+ \frac{29}{10} & \frac{7}{10} \\
+ \frac{1}{5} & \frac{8}{5} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 2. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 2: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{3}{10} & -\frac{13}{10} \\
+ -\frac{3}{10} & \frac{6}{5} & -\frac{9}{5} \\
+ \frac{13}{10} & -\frac{27}{10} & \frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{11}{5} \\
+ \frac{29}{10} & \frac{7}{10} \\
+ \frac{1}{5} & \frac{8}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{3}{10} & -\frac{13}{10} \\
+ -\frac{3}{10} & \frac{6}{5} & -\frac{9}{5} \\
+ \frac{13}{10} & -\frac{27}{10} & \frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{11}{5} \\
+ \frac{29}{10} & \frac{7}{10} \\
+ \frac{1}{5} & \frac{8}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{7}{5}\right)\, \times \, \frac{1}{5}+\frac{3\ 29}{10\ 10}+\left(-\frac{13}{10}\right)\, \times \, \frac{1}{5}=\frac{33}{100}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{3}{10} & -\frac{13}{10} \\
+ -\frac{3}{10} & \frac{6}{5} & -\frac{9}{5} \\
+ \frac{13}{10} & -\frac{27}{10} & \frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{11}{5} \\
+ \frac{29}{10} & \frac{7}{10} \\
+ \frac{1}{5} & \frac{8}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \fbox{$\frac{33}{100}$} & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{3}{10} & -\frac{13}{10} \\
+ -\frac{3}{10} & \frac{6}{5} & -\frac{9}{5} \\
+ \frac{13}{10} & -\frac{27}{10} & \frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{11}{5} \\
+ \frac{29}{10} & \frac{7}{10} \\
+ \frac{1}{5} & \frac{8}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{33}{100} & \_ \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{7}{5}\right)\, \times \, \frac{11}{5}+\frac{3\ 7}{10\ 10}+\left(-\frac{13}{10}\right)\, \times \, \frac{8}{5}=-\frac{99}{20}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{3}{10} & -\frac{13}{10} \\
+ -\frac{3}{10} & \frac{6}{5} & -\frac{9}{5} \\
+ \frac{13}{10} & -\frac{27}{10} & \frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{11}{5} \\
+ \frac{29}{10} & \frac{7}{10} \\
+ \frac{1}{5} & \frac{8}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{33}{100} & \fbox{$-\frac{99}{20}$} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{3}{10} & -\frac{13}{10} \\
+ -\frac{3}{10} & \frac{6}{5} & -\frac{9}{5} \\
+ \frac{13}{10} & -\frac{27}{10} & \frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{11}{5} \\
+ \frac{29}{10} & \frac{7}{10} \\
+ \frac{1}{5} & \frac{8}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{33}{100} & -\frac{99}{20} \\
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{3}{10}\right)\, \times \, \frac{1}{5}+\frac{6\ 29}{5\ 10}+\left(-\frac{9}{5}\right)\, \times \, \frac{1}{5}=\frac{153}{50}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{3}{10} & -\frac{13}{10} \\
+ -\frac{3}{10} & \frac{6}{5} & -\frac{9}{5} \\
+ \frac{13}{10} & -\frac{27}{10} & \frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{11}{5} \\
+ \frac{29}{10} & \frac{7}{10} \\
+ \frac{1}{5} & \frac{8}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{33}{100} & -\frac{99}{20} \\
+ \fbox{$\frac{153}{50}$} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{3}{10} & -\frac{13}{10} \\
+ -\frac{3}{10} & \frac{6}{5} & -\frac{9}{5} \\
+ \frac{13}{10} & -\frac{27}{10} & \frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{11}{5} \\
+ \frac{29}{10} & \frac{7}{10} \\
+ \frac{1}{5} & \frac{8}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{33}{100} & -\frac{99}{20} \\
+ \frac{153}{50} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{3}{10}\right)\, \times \, \frac{11}{5}+\frac{6\ 7}{5\ 10}+\left(-\frac{9}{5}\right)\, \times \, \frac{8}{5}=-\frac{27}{10}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{3}{10} & -\frac{13}{10} \\
+ -\frac{3}{10} & \frac{6}{5} & -\frac{9}{5} \\
+ \frac{13}{10} & -\frac{27}{10} & \frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{11}{5} \\
+ \frac{29}{10} & \frac{7}{10} \\
+ \frac{1}{5} & \frac{8}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{33}{100} & -\frac{99}{20} \\
+ \frac{153}{50} & \fbox{$-\frac{27}{10}$} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{3}{10} & -\frac{13}{10} \\
+ -\frac{3}{10} & \frac{6}{5} & -\frac{9}{5} \\
+ \frac{13}{10} & -\frac{27}{10} & \frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{11}{5} \\
+ \frac{29}{10} & \frac{7}{10} \\
+ \frac{1}{5} & \frac{8}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{33}{100} & -\frac{99}{20} \\
+ \frac{153}{50} & -\frac{27}{10} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{13}{10\ 5}+\left(-\frac{27}{10}\right)\, \times \, \frac{29}{10}+\frac{13}{5\ 5}=-\frac{141}{20}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{3}{10} & -\frac{13}{10} \\
+ -\frac{3}{10} & \frac{6}{5} & -\frac{9}{5} \\
+ \frac{13}{10} & -\frac{27}{10} & \frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{11}{5} \\
+ \frac{29}{10} & \frac{7}{10} \\
+ \frac{1}{5} & \frac{8}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{33}{100} & -\frac{99}{20} \\
+ \frac{153}{50} & -\frac{27}{10} \\
+ \fbox{$-\frac{141}{20}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{3}{10} & -\frac{13}{10} \\
+ -\frac{3}{10} & \frac{6}{5} & -\frac{9}{5} \\
+ \frac{13}{10} & -\frac{27}{10} & \frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{11}{5} \\
+ \frac{29}{10} & \frac{7}{10} \\
+ \frac{1}{5} & \frac{8}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{33}{100} & -\frac{99}{20} \\
+ \frac{153}{50} & -\frac{27}{10} \\
+ -\frac{141}{20} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{13\ 11}{10\ 5}+\left(-\frac{27}{10}\right)\, \times \, \frac{7}{10}+\frac{13\ 8}{5\ 5}=\frac{513}{100}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ -\frac{7}{5} & \frac{3}{10} & -\frac{13}{10} \\
+ -\frac{3}{10} & \frac{6}{5} & -\frac{9}{5} \\
+ \frac{13}{10} & -\frac{27}{10} & \frac{13}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ \frac{1}{5} & \frac{11}{5} \\
+ \frac{29}{10} & \frac{7}{10} \\
+ \frac{1}{5} & \frac{8}{5} \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \frac{33}{100} & -\frac{99}{20} \\
+ \frac{153}{50} & -\frac{27}{10} \\
+ -\frac{141}{20} & \fbox{$\frac{513}{100}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/4887.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/4887.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e992b076fdc61d9455911763981b8109a6dbe4d6
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/4887.txt
@@ -0,0 +1,549 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ 0 & 2 & -2 \\
+ 1 & -2 & -2 \\
+ 1 & 1 & 0 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ -3 & 2 & 2 \\
+ -2 & -2 & -1 \\
+ 2 & -3 & 1 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ 0 & 2 & -2 \\
+ 1 & -2 & -2 \\
+ 1 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -3 & 2 & 2 \\
+ -2 & -2 & -1 \\
+ 2 & -3 & 1 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 0 & 2 & -2 \\
+ 1 & -2 & -2 \\
+ 1 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -3 & 2 & 2 \\
+ -2 & -2 & -1 \\
+ 2 & -3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 0 & 2 & -2 \\
+ 1 & -2 & -2 \\
+ 1 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -3 & 2 & 2 \\
+ -2 & -2 & -1 \\
+ 2 & -3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0 (-3)+2 (-2)+(-2)\, \times \, 2=-8. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 0 & 2 & -2 \\
+ 1 & -2 & -2 \\
+ 1 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -3 & 2 & 2 \\
+ -2 & -2 & -1 \\
+ 2 & -3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$-8$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 0 & 2 & -2 \\
+ 1 & -2 & -2 \\
+ 1 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -3 & 2 & 2 \\
+ -2 & -2 & -1 \\
+ 2 & -3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -8 & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0\ 2+2 (-2)+(-2)\, (-3)=2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 0 & 2 & -2 \\
+ 1 & -2 & -2 \\
+ 1 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -3 & 2 & 2 \\
+ -2 & -2 & -1 \\
+ 2 & -3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -8 & \fbox{$2$} & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 0 & 2 & -2 \\
+ 1 & -2 & -2 \\
+ 1 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -3 & 2 & 2 \\
+ -2 & -2 & -1 \\
+ 2 & -3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -8 & 2 & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0\ 2+2 (-1)+(-2)\, \times \, 1=-4. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 0 & 2 & -2 \\
+ 1 & -2 & -2 \\
+ 1 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -3 & 2 & 2 \\
+ -2 & -2 & -1 \\
+ 2 & -3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -8 & 2 & \fbox{$-4$} \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 0 & 2 & -2 \\
+ 1 & -2 & -2 \\
+ 1 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -3 & 2 & 2 \\
+ -2 & -2 & -1 \\
+ 2 & -3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -8 & 2 & -4 \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1 (-3)+(-2)\, (-2)+(-2)\, \times \, 2=-3. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 0 & 2 & -2 \\
+ 1 & -2 & -2 \\
+ 1 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -3 & 2 & 2 \\
+ -2 & -2 & -1 \\
+ 2 & -3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -8 & 2 & -4 \\
+ \fbox{$-3$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 0 & 2 & -2 \\
+ 1 & -2 & -2 \\
+ 1 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -3 & 2 & 2 \\
+ -2 & -2 & -1 \\
+ 2 & -3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -8 & 2 & -4 \\
+ -3 & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1\ 2+(-2)\, (-2)+(-2)\, (-3)=12. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 0 & 2 & -2 \\
+ 1 & -2 & -2 \\
+ 1 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -3 & 2 & 2 \\
+ -2 & -2 & -1 \\
+ 2 & -3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -8 & 2 & -4 \\
+ -3 & \fbox{$12$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 0 & 2 & -2 \\
+ 1 & -2 & -2 \\
+ 1 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -3 & 2 & 2 \\
+ -2 & -2 & -1 \\
+ 2 & -3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -8 & 2 & -4 \\
+ -3 & 12 & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1\ 2+(-2)\, (-1)+(-2)\, \times \, 1=2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 0 & 2 & -2 \\
+ 1 & -2 & -2 \\
+ 1 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -3 & 2 & 2 \\
+ -2 & -2 & -1 \\
+ 2 & -3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -8 & 2 & -4 \\
+ -3 & 12 & \fbox{$2$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 0 & 2 & -2 \\
+ 1 & -2 & -2 \\
+ 1 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -3 & 2 & 2 \\
+ -2 & -2 & -1 \\
+ 2 & -3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -8 & 2 & -4 \\
+ -3 & 12 & 2 \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1 (-3)+1 (-2)+0\ 2=-5. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 0 & 2 & -2 \\
+ 1 & -2 & -2 \\
+ 1 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -3 & 2 & 2 \\
+ -2 & -2 & -1 \\
+ 2 & -3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -8 & 2 & -4 \\
+ -3 & 12 & 2 \\
+ \fbox{$-5$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 0 & 2 & -2 \\
+ 1 & -2 & -2 \\
+ 1 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -3 & 2 & 2 \\
+ -2 & -2 & -1 \\
+ 2 & -3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -8 & 2 & -4 \\
+ -3 & 12 & 2 \\
+ -5 & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1\ 2+1 (-2)+0 (-3)=0. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 0 & 2 & -2 \\
+ 1 & -2 & -2 \\
+ 1 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -3 & 2 & 2 \\
+ -2 & -2 & -1 \\
+ 2 & -3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -8 & 2 & -4 \\
+ -3 & 12 & 2 \\
+ -5 & \fbox{$0$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 0 & 2 & -2 \\
+ 1 & -2 & -2 \\
+ 1 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -3 & 2 & 2 \\
+ -2 & -2 & -1 \\
+ 2 & -3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -8 & 2 & -4 \\
+ -3 & 12 & 2 \\
+ -5 & 0 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1\ 2+1 (-1)+0\ 1=1. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ 0 & 2 & -2 \\
+ 1 & -2 & -2 \\
+ 1 & 1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -3 & 2 & 2 \\
+ -2 & -2 & -1 \\
+ 2 & -3 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -8 & 2 & -4 \\
+ -3 & 12 & 2 \\
+ -5 & 0 & \fbox{$1$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/561.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/561.txt
new file mode 100644
index 0000000000000000000000000000000000000000..854d38500bb8e497f6d1b870193b80d4040a2743
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/561.txt
@@ -0,0 +1,253 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ -1 & -3 \\
+ 3 & -2 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -2 & -2 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ -1 & -3 \\
+ 3 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -2 & -2 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 2. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 2: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -1 & -3 \\
+ 3 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -1 & -3 \\
+ 3 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \_ & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, \times \, 1+(-3)\, (-2)=5. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -1 & -3 \\
+ 3 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ \fbox{$5$} & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -1 & -3 \\
+ 3 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 5 & \_ \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, \times \, 1+(-3)\, (-2)=5. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -1 & -3 \\
+ 3 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 5 & \fbox{$5$} \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -1 & -3 \\
+ 3 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 5 & 5 \\
+ \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }3\ 1+(-2)\, (-2)=7. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -1 & -3 \\
+ 3 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 5 & 5 \\
+ \fbox{$7$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -1 & -3 \\
+ 3 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 5 & 5 \\
+ 7 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }3\ 1+(-2)\, (-2)=7. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ -1 & -3 \\
+ 3 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{cc}
+ 5 & 5 \\
+ 7 & \fbox{$7$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/602.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/602.txt
new file mode 100644
index 0000000000000000000000000000000000000000..23e9606de7df38722475a93860b05d178d5174b1
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/602.txt
@@ -0,0 +1,222 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ \frac{13}{5} & -\frac{6}{5} \\
+ -\frac{3}{5} & \frac{21}{10} \\
+ \frac{3}{5} & -\frac{9}{5} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ \frac{14}{5} \\
+ -\frac{21}{10} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ \frac{13}{5} & -\frac{6}{5} \\
+ -\frac{3}{5} & \frac{21}{10} \\
+ \frac{3}{5} & -\frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{14}{5} \\
+ -\frac{21}{10} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{13}{5} & -\frac{6}{5} \\
+ -\frac{3}{5} & \frac{21}{10} \\
+ \frac{3}{5} & -\frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{14}{5} \\
+ -\frac{21}{10} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{13}{5} & -\frac{6}{5} \\
+ -\frac{3}{5} & \frac{21}{10} \\
+ \frac{3}{5} & -\frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{14}{5} \\
+ -\frac{21}{10} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{13\ 14}{5\ 5}+\left(-\frac{6}{5}\right)\, \left(-\frac{21}{10}\right)=\frac{49}{5}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{13}{5} & -\frac{6}{5} \\
+ -\frac{3}{5} & \frac{21}{10} \\
+ \frac{3}{5} & -\frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{14}{5} \\
+ -\frac{21}{10} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$\frac{49}{5}$} \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{13}{5} & -\frac{6}{5} \\
+ -\frac{3}{5} & \frac{21}{10} \\
+ \frac{3}{5} & -\frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{14}{5} \\
+ -\frac{21}{10} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \frac{49}{5} \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{3}{5}\right)\, \times \, \frac{14}{5}+\frac{21 (-21)}{10\ 10}=-\frac{609}{100}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{13}{5} & -\frac{6}{5} \\
+ -\frac{3}{5} & \frac{21}{10} \\
+ \frac{3}{5} & -\frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{14}{5} \\
+ -\frac{21}{10} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \frac{49}{5} \\
+ \fbox{$-\frac{609}{100}$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{13}{5} & -\frac{6}{5} \\
+ -\frac{3}{5} & \frac{21}{10} \\
+ \frac{3}{5} & -\frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{14}{5} \\
+ -\frac{21}{10} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \frac{49}{5} \\
+ -\frac{609}{100} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{3\ 14}{5\ 5}+\left(-\frac{9}{5}\right)\, \left(-\frac{21}{10}\right)=\frac{273}{50}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ \frac{13}{5} & -\frac{6}{5} \\
+ -\frac{3}{5} & \frac{21}{10} \\
+ \frac{3}{5} & -\frac{9}{5} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ \frac{14}{5} \\
+ -\frac{21}{10} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \frac{49}{5} \\
+ -\frac{609}{100} \\
+ \fbox{$\frac{273}{50}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/612.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/612.txt
new file mode 100644
index 0000000000000000000000000000000000000000..225845e2f6367d010eb1c5b4fe7eb4fe6c9cb2c0
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/612.txt
@@ -0,0 +1,347 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ -\frac{17}{7} & -\frac{18}{7} \\
+ -\frac{13}{7} & -\frac{20}{7} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ -\frac{19}{7} & 0 & -\frac{16}{7} \\
+ \frac{4}{7} & \frac{11}{7} & -2 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{17}{7} & -\frac{18}{7} \\
+ -\frac{13}{7} & -\frac{20}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{19}{7} & 0 & -\frac{16}{7} \\
+ \frac{4}{7} & \frac{11}{7} & -2 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{17}{7} & -\frac{18}{7} \\
+ -\frac{13}{7} & -\frac{20}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{19}{7} & 0 & -\frac{16}{7} \\
+ \frac{4}{7} & \frac{11}{7} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{17}{7} & -\frac{18}{7} \\
+ -\frac{13}{7} & -\frac{20}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{19}{7} & 0 & -\frac{16}{7} \\
+ \frac{4}{7} & \frac{11}{7} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{17}{7}\right)\, \left(-\frac{19}{7}\right)+\left(-\frac{18}{7}\right)\, \times \, \frac{4}{7}=\frac{251}{49}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{17}{7} & -\frac{18}{7} \\
+ -\frac{13}{7} & -\frac{20}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{19}{7} & 0 & -\frac{16}{7} \\
+ \frac{4}{7} & \frac{11}{7} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$\frac{251}{49}$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{17}{7} & -\frac{18}{7} \\
+ -\frac{13}{7} & -\frac{20}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{19}{7} & 0 & -\frac{16}{7} \\
+ \frac{4}{7} & \frac{11}{7} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{251}{49} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{17}{7}\right)\, \times \, 0+\left(-\frac{18}{7}\right)\, \times \, \frac{11}{7}=-\frac{198}{49}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{17}{7} & -\frac{18}{7} \\
+ -\frac{13}{7} & -\frac{20}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{19}{7} & 0 & -\frac{16}{7} \\
+ \frac{4}{7} & \frac{11}{7} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{251}{49} & \fbox{$-\frac{198}{49}$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{17}{7} & -\frac{18}{7} \\
+ -\frac{13}{7} & -\frac{20}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{19}{7} & 0 & -\frac{16}{7} \\
+ \frac{4}{7} & \frac{11}{7} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{251}{49} & -\frac{198}{49} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{17}{7}\right)\, \left(-\frac{16}{7}\right)+\left(-\frac{18}{7}\right)\, (-2)=\frac{524}{49}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{17}{7} & -\frac{18}{7} \\
+ -\frac{13}{7} & -\frac{20}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{19}{7} & 0 & -\frac{16}{7} \\
+ \frac{4}{7} & \frac{11}{7} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{251}{49} & -\frac{198}{49} & \fbox{$\frac{524}{49}$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{17}{7} & -\frac{18}{7} \\
+ -\frac{13}{7} & -\frac{20}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{19}{7} & 0 & -\frac{16}{7} \\
+ \frac{4}{7} & \frac{11}{7} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{251}{49} & -\frac{198}{49} & \frac{524}{49} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{13}{7}\right)\, \left(-\frac{19}{7}\right)+\left(-\frac{20}{7}\right)\, \times \, \frac{4}{7}=\frac{167}{49}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{17}{7} & -\frac{18}{7} \\
+ -\frac{13}{7} & -\frac{20}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{19}{7} & 0 & -\frac{16}{7} \\
+ \frac{4}{7} & \frac{11}{7} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{251}{49} & -\frac{198}{49} & \frac{524}{49} \\
+ \fbox{$\frac{167}{49}$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{17}{7} & -\frac{18}{7} \\
+ -\frac{13}{7} & -\frac{20}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{19}{7} & 0 & -\frac{16}{7} \\
+ \frac{4}{7} & \frac{11}{7} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{251}{49} & -\frac{198}{49} & \frac{524}{49} \\
+ \frac{167}{49} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{13}{7}\right)\, \times \, 0+\left(-\frac{20}{7}\right)\, \times \, \frac{11}{7}=-\frac{220}{49}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ -\frac{17}{7} & -\frac{18}{7} \\
+ -\frac{13}{7} & -\frac{20}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{19}{7} & 0 & -\frac{16}{7} \\
+ \frac{4}{7} & \frac{11}{7} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{251}{49} & -\frac{198}{49} & \frac{524}{49} \\
+ \frac{167}{49} & \fbox{$-\frac{220}{49}$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ -\frac{17}{7} & -\frac{18}{7} \\
+ -\frac{13}{7} & -\frac{20}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{19}{7} & 0 & -\frac{16}{7} \\
+ \frac{4}{7} & \frac{11}{7} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{251}{49} & -\frac{198}{49} & \frac{524}{49} \\
+ \frac{167}{49} & -\frac{220}{49} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\left(-\frac{13}{7}\right)\, \left(-\frac{16}{7}\right)+\left(-\frac{20}{7}\right)\, (-2)=\frac{488}{49}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ -\frac{17}{7} & -\frac{18}{7} \\
+ -\frac{13}{7} & -\frac{20}{7} \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -\frac{19}{7} & 0 & -\frac{16}{7} \\
+ \frac{4}{7} & \frac{11}{7} & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \frac{251}{49} & -\frac{198}{49} & \frac{524}{49} \\
+ \frac{167}{49} & -\frac{220}{49} & \fbox{$\frac{488}{49}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/622.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/622.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e5691cb9fb39ed04c9b643d51b1692b251a772d5
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/622.txt
@@ -0,0 +1,222 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ 2 & 1 \\
+ -1 & 1 \\
+ 0 & -1 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 2 \\
+ -2 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ 2 & 1 \\
+ -1 & 1 \\
+ 0 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 2 \\
+ -2 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & 1 \\
+ -1 & 1 \\
+ 0 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 2 \\
+ -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & 1 \\
+ -1 & 1 \\
+ 0 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 2 \\
+ -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }2\ 2+1 (-2)=2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & 1 \\
+ -1 & 1 \\
+ 0 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 2 \\
+ -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$2$} \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & 1 \\
+ -1 & 1 \\
+ 0 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 2 \\
+ -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 2 \\
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, \times \, 2+1 (-2)=-4. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 2 & 1 \\
+ -1 & 1 \\
+ 0 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 2 \\
+ -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 2 \\
+ \fbox{$-4$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 2 & 1 \\
+ -1 & 1 \\
+ 0 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 2 \\
+ -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 2 \\
+ -4 \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }0\ 2+(-1)\, (-2)=2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ 2 & 1 \\
+ -1 & 1 \\
+ 0 & -1 \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ 2 \\
+ -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ 2 \\
+ -4 \\
+ \fbox{$2$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/738.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/738.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a5b9b4b2df75a3c4879e541203b5e8462431ff1e
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/738.txt
@@ -0,0 +1,549 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ -1 & 2 & -3 \\
+ -1 & 1 & -2 \\
+ -2 & 0 & 3 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ -2 & 1 & 2 \\
+ -1 & 1 & 1 \\
+ -1 & -2 & -2 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ -1 & 2 & -3 \\
+ -1 & 1 & -2 \\
+ -2 & 0 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & 2 \\
+ -1 & 1 & 1 \\
+ -1 & -2 & -2 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }3\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }3\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -1 & 2 & -3 \\
+ -1 & 1 & -2 \\
+ -2 & 0 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & 2 \\
+ -1 & 1 & 1 \\
+ -1 & -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -1 & 2 & -3 \\
+ -1 & 1 & -2 \\
+ -2 & 0 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & 2 \\
+ -1 & 1 & 1 \\
+ -1 & -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, (-2)+2 (-1)+(-3)\, (-1)=3. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -1 & 2 & -3 \\
+ -1 & 1 & -2 \\
+ -2 & 0 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & 2 \\
+ -1 & 1 & 1 \\
+ -1 & -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$3$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -1 & 2 & -3 \\
+ -1 & 1 & -2 \\
+ -2 & 0 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & 2 \\
+ -1 & 1 & 1 \\
+ -1 & -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 3 & \_ & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, \times \, 1+2\ 1+(-3)\, (-2)=7. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -1 & 2 & -3 \\
+ -1 & 1 & -2 \\
+ -2 & 0 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & 2 \\
+ -1 & 1 & 1 \\
+ -1 & -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 3 & \fbox{$7$} & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -1 & 2 & -3 \\
+ -1 & 1 & -2 \\
+ -2 & 0 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & 2 \\
+ -1 & 1 & 1 \\
+ -1 & -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 3 & 7 & \_ \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, \times \, 2+2\ 1+(-3)\, (-2)=6. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -1 & 2 & -3 \\
+ -1 & 1 & -2 \\
+ -2 & 0 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & 2 \\
+ -1 & 1 & 1 \\
+ -1 & -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 3 & 7 & \fbox{$6$} \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -1 & 2 & -3 \\
+ -1 & 1 & -2 \\
+ -2 & 0 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & 2 \\
+ -1 & 1 & 1 \\
+ -1 & -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 3 & 7 & 6 \\
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, (-2)+1 (-1)+(-2)\, (-1)=3. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -1 & 2 & -3 \\
+ -1 & 1 & -2 \\
+ -2 & 0 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & 2 \\
+ -1 & 1 & 1 \\
+ -1 & -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 3 & 7 & 6 \\
+ \fbox{$3$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -1 & 2 & -3 \\
+ -1 & 1 & -2 \\
+ -2 & 0 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & 2 \\
+ -1 & 1 & 1 \\
+ -1 & -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 3 & 7 & 6 \\
+ 3 & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, \times \, 1+1\ 1+(-2)\, (-2)=4. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -1 & 2 & -3 \\
+ -1 & 1 & -2 \\
+ -2 & 0 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & 2 \\
+ -1 & 1 & 1 \\
+ -1 & -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 3 & 7 & 6 \\
+ 3 & \fbox{$4$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -1 & 2 & -3 \\
+ -1 & 1 & -2 \\
+ -2 & 0 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & 2 \\
+ -1 & 1 & 1 \\
+ -1 & -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 3 & 7 & 6 \\
+ 3 & 4 & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, \times \, 2+1\ 1+(-2)\, (-2)=3. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -1 & 2 & -3 \\
+ -1 & 1 & -2 \\
+ -2 & 0 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & 2 \\
+ -1 & 1 & 1 \\
+ -1 & -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 3 & 7 & 6 \\
+ 3 & 4 & \fbox{$3$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -1 & 2 & -3 \\
+ -1 & 1 & -2 \\
+ -2 & 0 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & 2 \\
+ -1 & 1 & 1 \\
+ -1 & -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 3 & 7 & 6 \\
+ 3 & 4 & 3 \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, (-2)+0 (-1)+3 (-1)=1. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -1 & 2 & -3 \\
+ -1 & 1 & -2 \\
+ -2 & 0 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & 2 \\
+ -1 & 1 & 1 \\
+ -1 & -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 3 & 7 & 6 \\
+ 3 & 4 & 3 \\
+ \fbox{$1$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -1 & 2 & -3 \\
+ -1 & 1 & -2 \\
+ -2 & 0 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & 2 \\
+ -1 & 1 & 1 \\
+ -1 & -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 3 & 7 & 6 \\
+ 3 & 4 & 3 \\
+ 1 & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, \times \, 1+0\ 1+3 (-2)=-8. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ -1 & 2 & -3 \\
+ -1 & 1 & -2 \\
+ -2 & 0 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & 2 \\
+ -1 & 1 & 1 \\
+ -1 & -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 3 & 7 & 6 \\
+ 3 & 4 & 3 \\
+ 1 & \fbox{$-8$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }3^{\text{rd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ -1 & 2 & -3 \\
+ -1 & 1 & -2 \\
+ -2 & 0 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & 2 \\
+ -1 & 1 & 1 \\
+ -1 & -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 3 & 7 & 6 \\
+ 3 & 4 & 3 \\
+ 1 & -8 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-2)\, \times \, 2+0\ 1+3 (-2)=-10. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }3^{\text{rd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ -1 & 2 & -3 \\
+ -1 & 1 & -2 \\
+ -2 & 0 & 3 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 1 & 2 \\
+ -1 & 1 & 1 \\
+ -1 & -2 & -2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 3 & 7 & 6 \\
+ 3 & 4 & 3 \\
+ 1 & -8 & \fbox{$-10$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/739.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/739.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d6121f1b228eaf7f83a84ca3a7965170eeed8e77
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/739.txt
@@ -0,0 +1,159 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ \frac{13}{16} & \frac{3}{16} \\
+ \frac{43}{16} & -\frac{33}{16} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -\frac{9}{8} \\
+ \frac{43}{16} \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ \frac{13}{16} & \frac{3}{16} \\
+ \frac{43}{16} & -\frac{33}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -\frac{9}{8} \\
+ \frac{43}{16} \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 1. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 1: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{13}{16} & \frac{3}{16} \\
+ \frac{43}{16} & -\frac{33}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -\frac{9}{8} \\
+ \frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{13}{16} & \frac{3}{16} \\
+ \frac{43}{16} & -\frac{33}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -\frac{9}{8} \\
+ \frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \_ \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{13 (-9)}{16\ 8}+\frac{3\ 43}{16\ 16}=-\frac{105}{256}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ \frac{13}{16} & \frac{3}{16} \\
+ \frac{43}{16} & -\frac{33}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -\frac{9}{8} \\
+ \frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ \fbox{$-\frac{105}{256}$} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ \frac{13}{16} & \frac{3}{16} \\
+ \frac{43}{16} & -\frac{33}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -\frac{9}{8} \\
+ \frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ -\frac{105}{256} \\
+ \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }\frac{43 (-9)}{16\ 8}+\left(-\frac{33}{16}\right)\, \times \, \frac{43}{16}=-\frac{2193}{256}. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ \frac{13}{16} & \frac{3}{16} \\
+ \frac{43}{16} & -\frac{33}{16} \\
+\end{array}
+\right).\left(
+\begin{array}{c}
+ -\frac{9}{8} \\
+ \frac{43}{16} \\
+\end{array}
+\right)=\left(
+\begin{array}{c}
+ -\frac{105}{256} \\
+ \fbox{$-\frac{2193}{256}$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/758.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/758.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0062b1b643a9bd3b30c0cf9ef8b4f1139593457f
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/758.txt
@@ -0,0 +1,362 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{ccc}
+ 3 & 2 & 0 \\
+ 3 & -1 & -2 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ 3 & 3 & -1 \\
+ -1 & 1 & -2 \\
+ -3 & -2 & 1 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{ccc}
+ 3 & 2 & 0 \\
+ 3 & -1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 3 & 3 & -1 \\
+ -1 & 1 & -2 \\
+ -3 & -2 & 1 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 3 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }3\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 3 & 2 & 0 \\
+ 3 & -1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 3 & 3 & -1 \\
+ -1 & 1 & -2 \\
+ -3 & -2 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 3 & 2 & 0 \\
+ 3 & -1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 3 & 3 & -1 \\
+ -1 & 1 & -2 \\
+ -3 & -2 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }3\ 3+2 (-1)+0 (-3)=7. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 3 & 2 & 0 \\
+ 3 & -1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 3 & 3 & -1 \\
+ -1 & 1 & -2 \\
+ -3 & -2 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$7$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 3 & 2 & 0 \\
+ 3 & -1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 3 & 3 & -1 \\
+ -1 & 1 & -2 \\
+ -3 & -2 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 7 & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }3\ 3+2\ 1+0 (-2)=11. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 3 & 2 & 0 \\
+ 3 & -1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 3 & 3 & -1 \\
+ -1 & 1 & -2 \\
+ -3 & -2 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 7 & \fbox{$11$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 3 & 2 & 0 \\
+ 3 & -1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 3 & 3 & -1 \\
+ -1 & 1 & -2 \\
+ -3 & -2 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 7 & 11 & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }3 (-1)+2 (-2)+0\ 1=-7. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 3 & 2 & 0 \\
+ 3 & -1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 3 & 3 & -1 \\
+ -1 & 1 & -2 \\
+ -3 & -2 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 7 & 11 & \fbox{$-7$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 3 & 2 & 0 \\
+ 3 & -1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 3 & 3 & -1 \\
+ -1 & 1 & -2 \\
+ -3 & -2 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 7 & 11 & -7 \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }3\ 3+(-1)\, (-1)+(-2)\, (-3)=16. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 3 & 2 & 0 \\
+ 3 & -1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 3 & 3 & -1 \\
+ -1 & 1 & -2 \\
+ -3 & -2 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 7 & 11 & -7 \\
+ \fbox{$16$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 3 & 2 & 0 \\
+ 3 & -1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 3 & 3 & -1 \\
+ -1 & 1 & -2 \\
+ -3 & -2 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 7 & 11 & -7 \\
+ 16 & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }3\ 3+(-1)\, \times \, 1+(-2)\, (-2)=12. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{ccc}
+ 3 & 2 & 0 \\
+ 3 & -1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 3 & 3 & -1 \\
+ -1 & 1 & -2 \\
+ -3 & -2 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 7 & 11 & -7 \\
+ 16 & \fbox{$12$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{ccc}
+ 3 & 2 & 0 \\
+ 3 & -1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 3 & 3 & -1 \\
+ -1 & 1 & -2 \\
+ -3 & -2 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 7 & 11 & -7 \\
+ 16 & 12 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }3 (-1)+(-1)\, (-2)+(-2)\, \times \, 1=-3. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{ccc}
+ 3 & 2 & 0 \\
+ 3 & -1 & -2 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ 3 & 3 & -1 \\
+ -1 & 1 & -2 \\
+ -3 & -2 & 1 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ 7 & 11 & -7 \\
+ 16 & 12 & \fbox{$-3$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file
diff --git a/pretraining/mathematica/linear_algebra/multiply_w_steps/864.txt b/pretraining/mathematica/linear_algebra/multiply_w_steps/864.txt
new file mode 100644
index 0000000000000000000000000000000000000000..34a89a6b5e5cde59a5e71d3b585845cc14fcd6d8
--- /dev/null
+++ b/pretraining/mathematica/linear_algebra/multiply_w_steps/864.txt
@@ -0,0 +1,347 @@
+Problem:
+Multiply
+$\left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -1 & 0 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{ccc}
+ -2 & 0 & 1 \\
+ -3 & -2 & 2 \\
+\end{array}
+\right)$.
+Answer:
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply the following matrices}: \\
+ \left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 0 & 1 \\
+ -3 & -2 & 2 \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+\hline
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{The }\text{dimensions }\text{of }\text{the }\text{first }\text{matrix }\text{are }2\times 2 \text{and }\text{the }\text{dimensions }\text{of }\text{the }\text{second }\text{matrix }\text{are }2\times 3. \\
+ \text{This }\text{means }\text{the }\text{dimensions }\text{of }\text{the }\text{product }\text{are }2\times 3: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 0 & 1 \\
+ -3 & -2 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 0 & 1 \\
+ -3 & -2 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \_ & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1 (-2)+1 (-3)=-5. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 0 & 1 \\
+ -3 & -2 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ \fbox{$-5$} & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 0 & 1 \\
+ -3 & -2 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & \_ & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1\ 0+1 (-2)=-2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 0 & 1 \\
+ -3 & -2 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & \fbox{$-2$} & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }1^{\text{st}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 0 & 1 \\
+ -3 & -2 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -2 & \_ \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }1\ 1+1\ 2=3. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }1^{\text{st}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 0 & 1 \\
+ -3 & -2 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -2 & \fbox{$3$} \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }1^{\text{st}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 0 & 1 \\
+ -3 & -2 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -2 & 3 \\
+ \_ & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, (-2)+0 (-3)=2. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }1^{\text{st}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 0 & 1 \\
+ -3 & -2 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -2 & 3 \\
+ \fbox{$2$} & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }2^{\text{nd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 0 & 1 \\
+ -3 & -2 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -2 & 3 \\
+ 2 & \_ & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, \times \, 0+0 (-2)=0. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }2^{\text{nd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 0 & 1 \\
+ -3 & -2 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -2 & 3 \\
+ 2 & \fbox{$0$} & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ \text{Highlight }\text{the }2^{\text{nd}} \text{row }\text{and }\text{the }3^{\text{rd}} \text{column}: \\
+ \left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 0 & 1 \\
+ -3 & -2 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -2 & 3 \\
+ 2 & 0 & \_ \\
+\end{array}
+\right) \\
+\end{array}
+ \\
+ 
+\begin{array}{l}
+ 
+\begin{array}{l}
+ \text{Multiply }\text{corresponding }\text{components }\text{and }\text{add: }(-1)\, \times \, 1+0\ 2=-1. \\
+ \text{Place }\text{this }\text{number }\text{into }\text{the }2^{\text{nd}} \text{row }\text{and }3^{\text{rd}} \text{column }\text{of }\text{the }\text{product}: \\
+\end{array}
+ \\
+ \fbox{$
+\begin{array}{ll}
+ \text{Answer:} &  \\
+ \text{} & \left(
+\begin{array}{cc}
+ 1 & 1 \\
+ -1 & 0 \\
+\end{array}
+\right).\left(
+\begin{array}{ccc}
+ -2 & 0 & 1 \\
+ -3 & -2 & 2 \\
+\end{array}
+\right)=\left(
+\begin{array}{ccc}
+ -5 & -2 & 3 \\
+ 2 & 0 & \fbox{$-1$} \\
+\end{array}
+\right) \\
+\end{array}
+$} \\
+\end{array}
+ \\
+\end{array}
\ No newline at end of file