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pretraining/mathematica/linear_algebra/row_reduce/10257.txt

@@ -0,0 +1,25 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{ccccc}
+ 2 & -6 & -1 & -8 & 1 \\
+ -3 & 2 & -7 & 10 & 4 \\
+ -5 & 7 & -9 & -1 & 5 \\
+ 10 & -6 & 5 & -3 & -4 \\
+ 3 & -8 & -7 & -7 & 2 \\
+ 7 & 8 & 4 & -3 & 7 \\
+ -2 & -10 & 5 & 7 & 0 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{ccccc}
+ 1 & 0 & 0 & 0 & 0 \\
+ 0 & 1 & 0 & 0 & 0 \\
+ 0 & 0 & 1 & 0 & 0 \\
+ 0 & 0 & 0 & 1 & 0 \\
+ 0 & 0 & 0 & 0 & 1 \\
+ 0 & 0 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 0 & 0 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/10437.txt

@@ -0,0 +1,21 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{ccccccc}
+ 1 & -4 & 2 & 9 & 9 & -6 & 2 \\
+ 8 & 6 & -2 & 10 & -7 & -3 & -6 \\
+ 6 & -1 & -9 & 7 & -5 & 5 & 2 \\
+ 3 & 7 & 3 & 1 & -8 & 5 & -2 \\
+ -8 & 4 & 6 & 9 & -5 & -8 & -10 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{ccccccc}
+ 1 & 0 & 0 & 0 & 0 & \frac{13227}{5627} & \frac{10094}{5627} \\
+ 0 & 1 & 0 & 0 & 0 & -\frac{138375}{22508} & -\frac{51707}{11254} \\
+ 0 & 0 & 1 & 0 & 0 & \frac{77589}{22508} & \frac{27589}{11254} \\
+ 0 & 0 & 0 & 1 & 0 & -\frac{5963}{11254} & -\frac{1929}{5627} \\
+ 0 & 0 & 0 & 0 & 1 & -\frac{21925}{5627} & -\frac{12498}{5627} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/11114.txt

@@ -0,0 +1,25 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cc}
+ -6 & -10 \\
+ -9 & -6 \\
+ -7 & 10 \\
+ 6 & 4 \\
+ 2 & -4 \\
+ 6 & -10 \\
+ -4 & -8 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ 0 & 1 \\
+ 0 & 0 \\
+ 0 & 0 \\
+ 0 & 0 \\
+ 0 & 0 \\
+ 0 & 0 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/11343.txt

@@ -0,0 +1,15 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccc}
+ 7 & -8 & -5 & 9 \\
+ 7 & -7 & 3 & -6 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccc}
+ 1 & 0 & \frac{59}{7} & -\frac{111}{7} \\
+ 0 & 1 & 8 & -15 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/1163.txt

@@ -0,0 +1,17 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccccc}
+ -5 & -3 & 5 & 8 & -10 & 6 \\
+ 8 & 9 & 6 & 9 & -4 & 3 \\
+ 5 & 4 & -6 & 9 & -4 & 10 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccccc}
+ 1 & 0 & 0 & -\frac{1173}{91} & \frac{1024}{91} & -12 \\
+ 0 & 1 & 0 & \frac{1299}{91} & -\frac{1080}{91} & 13 \\
+ 0 & 0 & 1 & -\frac{248}{91} & \frac{194}{91} & -3 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/12477.txt

@@ -0,0 +1,17 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccccc}
+ 6 & -9 & -2 & 4 & -1 & -7 \\
+ 3 & -8 & -10 & 6 & -5 & -8 \\
+ 5 & -4 & -3 & -4 & 3 & -3 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccccc}
+ 1 & 0 & 0 & -\frac{474}{217} & \frac{333}{217} & \frac{6}{31} \\
+ 0 & 1 & 0 & -\frac{428}{217} & \frac{243}{217} & \frac{27}{31} \\
+ 0 & 0 & 1 & \frac{10}{31} & \frac{2}{31} & \frac{5}{31} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/12672.txt

@@ -0,0 +1,25 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccccc}
+ 7 & -8 & -3 & 2 & -1 & -9 \\
+ 1 & 8 & 5 & -10 & 4 & -8 \\
+ -9 & 8 & 10 & 7 & -7 & -9 \\
+ 9 & -4 & 2 & -8 & 6 & -3 \\
+ -7 & -1 & -10 & 0 & 10 & 10 \\
+ -10 & 4 & -3 & 5 & -9 & -4 \\
+ -2 & -5 & 8 & -1 & -8 & -1 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccccc}
+ 1 & 0 & 0 & 0 & 0 & 0 \\
+ 0 & 1 & 0 & 0 & 0 & 0 \\
+ 0 & 0 & 1 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 1 & 0 & 0 \\
+ 0 & 0 & 0 & 0 & 1 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 1 \\
+ 0 & 0 & 0 & 0 & 0 & 0 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/14842.txt

@@ -0,0 +1,19 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{ccccccc}
+ 7 & 10 & -2 & 7 & -5 & 9 & -6 \\
+ 2 & -8 & 1 & -6 & 5 & 7 & -9 \\
+ 6 & 10 & 9 & 3 & 5 & -1 & 9 \\
+ 2 & 3 & 3 & 10 & 2 & -8 & 4 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{ccccccc}
+ 1 & 0 & 0 & 0 & \frac{527}{2553} & \frac{13327}{7659} & -\frac{13090}{7659} \\
+ 0 & 1 & 0 & 0 & -\frac{401}{851} & \frac{55}{851} & \frac{639}{851} \\
+ 0 & 0 & 1 & 0 & \frac{2387}{2553} & -\frac{8117}{7659} & \frac{9641}{7659} \\
+ 0 & 0 & 0 & 1 & \frac{50}{2553} & -\frac{6506}{7659} & \frac{1064}{7659} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/15771.txt

@@ -0,0 +1,15 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccccc}
+ 2 & -3 & -3 & 10 & -1 & 10 \\
+ 4 & -4 & -5 & 2 & 3 & -10 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccccc}
+ 1 & 0 & -\frac{3}{4} & -\frac{17}{2} & \frac{13}{4} & -\frac{35}{2} \\
+ 0 & 1 & \frac{1}{2} & -9 & \frac{5}{2} & -15 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/18261.txt

@@ -0,0 +1,25 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccccc}
+ 4 & 3 & 0 & 4 & 10 & -4 \\
+ 1 & 4 & -9 & 10 & 2 & -6 \\
+ -4 & -9 & 4 & 5 & -5 & 3 \\
+ 5 & -8 & 4 & 7 & 2 & 0 \\
+ -7 & 5 & 0 & 3 & 0 & 6 \\
+ 3 & -5 & 0 & -1 & 4 & 10 \\
+ 1 & -6 & 9 & -1 & 4 & 9 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccccc}
+ 1 & 0 & 0 & 0 & 0 & 0 \\
+ 0 & 1 & 0 & 0 & 0 & 0 \\
+ 0 & 0 & 1 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 1 & 0 & 0 \\
+ 0 & 0 & 0 & 0 & 1 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 1 \\
+ 0 & 0 & 0 & 0 & 0 & 0 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/18471.txt

@@ -0,0 +1,25 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cc}
+ -4 & -3 \\
+ 10 & 6 \\
+ -6 & -5 \\
+ -2 & 7 \\
+ -1 & 6 \\
+ -2 & -3 \\
+ 6 & -10 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ 0 & 1 \\
+ 0 & 0 \\
+ 0 & 0 \\
+ 0 & 0 \\
+ 0 & 0 \\
+ 0 & 0 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/18665.txt

@@ -0,0 +1,15 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccccc}
+ 8 & 4 & -10 & -7 & 3 & -4 \\
+ 5 & -4 & 10 & 10 & -6 & 9 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccccc}
+ 1 & 0 & 0 & \frac{3}{13} & -\frac{3}{13} & \frac{5}{13} \\
+ 0 & 1 & -\frac{5}{2} & -\frac{115}{52} & \frac{63}{52} & -\frac{23}{13} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/19349.txt

@@ -0,0 +1,23 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{ccccccc}
+ 6 & -6 & -5 & -6 & -6 & -10 & 1 \\
+ 6 & -3 & 1 & 0 & -10 & -7 & 6 \\
+ -8 & 4 & 4 & 3 & -2 & -8 & 0 \\
+ -8 & -3 & 4 & -1 & 5 & 4 & -7 \\
+ -6 & -1 & 9 & -7 & 7 & 4 & -6 \\
+ 7 & 8 & 1 & -9 & -2 & -8 & 4 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{ccccccc}
+ 1 & 0 & 0 & 0 & 0 & 0 & \frac{16261}{14461} \\
+ 0 & 1 & 0 & 0 & 0 & 0 & -\frac{1208}{101227} \\
+ 0 & 0 & 1 & 0 & 0 & 0 & \frac{62819}{101227} \\
+ 0 & 0 & 0 & 1 & 0 & 0 & \frac{92434}{101227} \\
+ 0 & 0 & 0 & 0 & 1 & 0 & \frac{58249}{101227} \\
+ 0 & 0 & 0 & 0 & 0 & 1 & -\frac{62921}{101227} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/19633.txt

@@ -0,0 +1,25 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{ccccccc}
+ 8 & 10 & 1 & 9 & -5 & 8 & -7 \\
+ 7 & 4 & 7 & -2 & -1 & -10 & 1 \\
+ 5 & -9 & 10 & 8 & 0 & 0 & 9 \\
+ 9 & 4 & -5 & -8 & 8 & 8 & 1 \\
+ -1 & 10 & 8 & -3 & 6 & -7 & 7 \\
+ 10 & 4 & 7 & -4 & 3 & 9 & 1 \\
+ 1 & -6 & -8 & -10 & -8 & 6 & 6 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{ccccccc}
+ 1 & 0 & 0 & 0 & 0 & 0 & 0 \\
+ 0 & 1 & 0 & 0 & 0 & 0 & 0 \\
+ 0 & 0 & 1 & 0 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 1 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 0 & 1 & 0 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 1 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 0 & 1 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/20376.txt

@@ -0,0 +1,15 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{ccccc}
+ 5 & 7 & -4 & 5 & 3 \\
+ -1 & 4 & 4 & -9 & 4 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{ccccc}
+ 1 & 0 & -\frac{44}{27} & \frac{83}{27} & -\frac{16}{27} \\
+ 0 & 1 & \frac{16}{27} & -\frac{40}{27} & \frac{23}{27} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/20580.txt

@@ -0,0 +1,23 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccc}
+ 9 & -7 & -2 & 1 \\
+ -7 & -3 & 0 & -1 \\
+ 4 & 10 & 9 & 1 \\
+ 10 & -2 & -3 & -6 \\
+ -5 & -6 & -9 & -8 \\
+ -4 & 2 & -2 & -5 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccc}
+ 1 & 0 & 0 & 0 \\
+ 0 & 1 & 0 & 0 \\
+ 0 & 0 & 1 & 0 \\
+ 0 & 0 & 0 & 1 \\
+ 0 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 0 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/20645.txt

@@ -0,0 +1,23 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccccc}
+ 3 & 6 & -10 & 2 & -2 & 5 \\
+ -10 & -9 & 4 & 7 & -10 & -7 \\
+ 9 & 7 & 5 & 0 & -10 & 5 \\
+ 10 & -8 & -9 & -10 & 10 & -2 \\
+ 0 & 9 & 2 & 3 & -7 & -1 \\
+ -2 & 8 & 8 & 10 & -2 & 1 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccccc}
+ 1 & 0 & 0 & 0 & 0 & 0 \\
+ 0 & 1 & 0 & 0 & 0 & 0 \\
+ 0 & 0 & 1 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 1 & 0 & 0 \\
+ 0 & 0 & 0 & 0 & 1 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 1 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/2109.txt

@@ -0,0 +1,19 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cc}
+ -3 & 4 \\
+ 3 & -6 \\
+ 4 & 5 \\
+ 8 & 5 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ 0 & 1 \\
+ 0 & 0 \\
+ 0 & 0 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/21464.txt

@@ -0,0 +1,15 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccccc}
+ 3 & 0 & 8 & -7 & -3 & 3 \\
+ 8 & 6 & -4 & 3 & -2 & 1 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccccc}
+ 1 & 0 & \frac{8}{3} & -\frac{7}{3} & -1 & 1 \\
+ 0 & 1 & -\frac{38}{9} & \frac{65}{18} & 1 & -\frac{7}{6} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/21500.txt

@@ -0,0 +1,23 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cc}
+ 4 & -9 \\
+ -4 & -9 \\
+ -3 & 6 \\
+ -3 & 1 \\
+ 9 & 3 \\
+ 8 & -2 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ 0 & 1 \\
+ 0 & 0 \\
+ 0 & 0 \\
+ 0 & 0 \\
+ 0 & 0 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/21582.txt

@@ -0,0 +1,19 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cc}
+ -7 & 1 \\
+ 10 & -2 \\
+ 10 & -4 \\
+ 6 & 5 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ 0 & 1 \\
+ 0 & 0 \\
+ 0 & 0 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/22247.txt

@@ -0,0 +1,17 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccccc}
+ -6 & -6 & 2 & -7 & 0 & 9 \\
+ -4 & 10 & 5 & -9 & -4 & 2 \\
+ -10 & 6 & -2 & -4 & -7 & 4 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccccc}
+ 1 & 0 & 0 & \frac{11}{16} & \frac{7}{16} & -\frac{13}{16} \\
+ 0 & 1 & 0 & \frac{3}{80} & -\frac{141}{400} & -\frac{37}{80} \\
+ 0 & 0 & 1 & -\frac{53}{40} & \frac{51}{200} & \frac{27}{40} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/23161.txt

@@ -0,0 +1,17 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{ccccc}
+ 1 & 8 & -3 & 0 & 6 \\
+ -7 & -7 & 6 & 0 & 2 \\
+ -10 & -8 & 4 & -10 & 10 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{ccccc}
+ 1 & 0 & 0 & \frac{135}{97} & -\frac{187}{97} \\
+ 0 & 1 & 0 & \frac{75}{97} & \frac{47}{97} \\
+ 0 & 0 & 1 & \frac{245}{97} & -\frac{131}{97} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/23329.txt

@@ -0,0 +1,15 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cc}
+ -7 & -8 \\
+ 4 & -10 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ 0 & 1 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/23684.txt

@@ -0,0 +1,25 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{ccccccc}
+ 10 & 7 & -4 & 1 & -4 & -1 & 2 \\
+ -10 & -7 & -7 & 5 & 10 & -3 & 4 \\
+ -7 & 2 & 7 & 3 & -7 & -3 & -7 \\
+ 4 & -8 & -3 & -5 & 10 & -8 & 4 \\
+ -2 & 4 & -6 & 9 & 2 & 1 & 10 \\
+ -3 & 6 & 10 & -8 & 2 & -10 & 7 \\
+ -8 & -5 & 2 & -9 & -8 & -5 & 6 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{ccccccc}
+ 1 & 0 & 0 & 0 & 0 & 0 & 0 \\
+ 0 & 1 & 0 & 0 & 0 & 0 & 0 \\
+ 0 & 0 & 1 & 0 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 1 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 0 & 1 & 0 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 1 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 0 & 1 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/23755.txt

@@ -0,0 +1,21 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccc}
+ -10 & -2 & -7 & -9 \\
+ 6 & 1 & -9 & 8 \\
+ 4 & -3 & 10 & 5 \\
+ -7 & 6 & 1 & 7 \\
+ 7 & -2 & 3 & -3 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccc}
+ 1 & 0 & 0 & 0 \\
+ 0 & 1 & 0 & 0 \\
+ 0 & 0 & 1 & 0 \\
+ 0 & 0 & 0 & 1 \\
+ 0 & 0 & 0 & 0 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/23762.txt

@@ -0,0 +1,21 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccccc}
+ 7 & -10 & 2 & 0 & -9 & -1 \\
+ 8 & -9 & -7 & 0 & 3 & 7 \\
+ -9 & -4 & 2 & -1 & -4 & -7 \\
+ -7 & -6 & 3 & -1 & 7 & 0 \\
+ -5 & 0 & 3 & -10 & 0 & -9 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccccc}
+ 1 & 0 & 0 & 0 & 0 & \frac{63369}{133198} \\
+ 0 & 1 & 0 & 0 & 0 & -\frac{5435}{66599} \\
+ 0 & 0 & 1 & 0 & 0 & -\frac{15649}{133198} \\
+ 0 & 0 & 0 & 1 & 0 & \frac{6423}{10246} \\
+ 0 & 0 & 0 & 0 & 1 & \frac{72687}{133198} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/24111.txt

@@ -0,0 +1,23 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccc}
+ -5 & 8 & -5 & 7 \\
+ -6 & 0 & 7 & 7 \\
+ -7 & 3 & 4 & 10 \\
+ 4 & -6 & 7 & -10 \\
+ 7 & -10 & -4 & -1 \\
+ -10 & -6 & 0 & -6 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccc}
+ 1 & 0 & 0 & 0 \\
+ 0 & 1 & 0 & 0 \\
+ 0 & 0 & 1 & 0 \\
+ 0 & 0 & 0 & 1 \\
+ 0 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 0 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/26090.txt

@@ -0,0 +1,25 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cc}
+ 5 & -5 \\
+ -1 & 2 \\
+ -6 & -2 \\
+ 5 & 3 \\
+ 8 & 2 \\
+ 0 & -5 \\
+ -3 & -3 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ 0 & 1 \\
+ 0 & 0 \\
+ 0 & 0 \\
+ 0 & 0 \\
+ 0 & 0 \\
+ 0 & 0 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/26166.txt

@@ -0,0 +1,19 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{ccc}
+ 9 & 7 & 6 \\
+ 1 & -9 & 2 \\
+ -4 & -6 & -10 \\
+ 4 & -3 & -7 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{ccc}
+ 1 & 0 & 0 \\
+ 0 & 1 & 0 \\
+ 0 & 0 & 1 \\
+ 0 & 0 & 0 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/28340.txt

@@ -0,0 +1,25 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{ccccc}
+ 10 & -1 & -9 & -2 & 6 \\
+ -10 & -5 & 2 & 3 & 1 \\
+ -4 & -9 & -3 & -2 & -9 \\
+ 1 & 6 & 0 & 10 & -7 \\
+ -10 & 5 & 3 & 7 & -2 \\
+ -7 & 4 & 4 & -10 & 4 \\
+ -9 & 1 & -4 & -10 & -1 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{ccccc}
+ 1 & 0 & 0 & 0 & 0 \\
+ 0 & 1 & 0 & 0 & 0 \\
+ 0 & 0 & 1 & 0 & 0 \\
+ 0 & 0 & 0 & 1 & 0 \\
+ 0 & 0 & 0 & 0 & 1 \\
+ 0 & 0 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 0 & 0 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/2843.txt

@@ -0,0 +1,15 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccccc}
+ -8 & -7 & 7 & 8 & 8 & 9 \\
+ 2 & -4 & -3 & 9 & 10 & 6 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccccc}
+ 1 & 0 & -\frac{49}{46} & \frac{31}{46} & \frac{19}{23} & \frac{3}{23} \\
+ 0 & 1 & \frac{5}{23} & -\frac{44}{23} & -\frac{48}{23} & -\frac{33}{23} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/29189.txt

@@ -0,0 +1,17 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cc}
+ -6 & 1 \\
+ 2 & 8 \\
+ -7 & -7 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ 0 & 1 \\
+ 0 & 0 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/29788.txt

@@ -0,0 +1,23 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccc}
+ 10 & -8 & -3 & 9 \\
+ 4 & -10 & -7 & -10 \\
+ 0 & 0 & -5 & 1 \\
+ -2 & -5 & -5 & 4 \\
+ 1 & 1 & -3 & 1 \\
+ -2 & 7 & 9 & 6 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccc}
+ 1 & 0 & 0 & 0 \\
+ 0 & 1 & 0 & 0 \\
+ 0 & 0 & 1 & 0 \\
+ 0 & 0 & 0 & 1 \\
+ 0 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 0 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/31029.txt

@@ -0,0 +1,23 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{ccccc}
+ 4 & -4 & 1 & -4 & 9 \\
+ -9 & -7 & 2 & -6 & 0 \\
+ 10 & 4 & 9 & 10 & 8 \\
+ -6 & 1 & 5 & -3 & 3 \\
+ 8 & -5 & 5 & 3 & 10 \\
+ 1 & 0 & 5 & -4 & 8 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{ccccc}
+ 1 & 0 & 0 & 0 & 0 \\
+ 0 & 1 & 0 & 0 & 0 \\
+ 0 & 0 & 1 & 0 & 0 \\
+ 0 & 0 & 0 & 1 & 0 \\
+ 0 & 0 & 0 & 0 & 1 \\
+ 0 & 0 & 0 & 0 & 0 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/31174.txt

@@ -0,0 +1,15 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccccc}
+ 5 & 4 & -4 & -6 & -9 & -2 \\
+ -4 & 3 & -9 & 4 & 3 & 5 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccccc}
+ 1 & 0 & \frac{24}{31} & -\frac{34}{31} & -\frac{39}{31} & -\frac{26}{31} \\
+ 0 & 1 & -\frac{61}{31} & -\frac{4}{31} & -\frac{21}{31} & \frac{17}{31} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/32566.txt

@@ -0,0 +1,21 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{ccccc}
+ 7 & 5 & 1 & -9 & -2 \\
+ -7 & -2 & 4 & 9 & 5 \\
+ -2 & 7 & -1 & -2 & -3 \\
+ 6 & -2 & -8 & -1 & -3 \\
+ 0 & 6 & 7 & 6 & 7 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{ccccc}
+ 1 & 0 & 0 & 0 & 0 \\
+ 0 & 1 & 0 & 0 & 0 \\
+ 0 & 0 & 1 & 0 & 0 \\
+ 0 & 0 & 0 & 1 & 0 \\
+ 0 & 0 & 0 & 0 & 1 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/33479.txt

@@ -0,0 +1,17 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{ccc}
+ -3 & -2 & 7 \\
+ -8 & 2 & -2 \\
+ 3 & -3 & -5 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{ccc}
+ 1 & 0 & 0 \\
+ 0 & 1 & 0 \\
+ 0 & 0 & 1 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/34818.txt

@@ -0,0 +1,25 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{ccccc}
+ 1 & -9 & 4 & 7 & -5 \\
+ -2 & 7 & -1 & 1 & -5 \\
+ 1 & 7 & 9 & 1 & -2 \\
+ -6 & -1 & -9 & -7 & -8 \\
+ 8 & -5 & 10 & 9 & 10 \\
+ -8 & 6 & 7 & -6 & -1 \\
+ 7 & 7 & 7 & -6 & -5 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{ccccc}
+ 1 & 0 & 0 & 0 & 0 \\
+ 0 & 1 & 0 & 0 & 0 \\
+ 0 & 0 & 1 & 0 & 0 \\
+ 0 & 0 & 0 & 1 & 0 \\
+ 0 & 0 & 0 & 0 & 1 \\
+ 0 & 0 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 0 & 0 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/34931.txt

@@ -0,0 +1,17 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cc}
+ 7 & 7 \\
+ 2 & 2 \\
+ -10 & -2 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ 0 & 1 \\
+ 0 & 0 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/36564.txt

@@ -0,0 +1,25 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccc}
+ -2 & -5 & -7 & -1 \\
+ 5 & -2 & -1 & 0 \\
+ -6 & -10 & 3 & -10 \\
+ 6 & 10 & -1 & 4 \\
+ -9 & 8 & -5 & 1 \\
+ 7 & 3 & -10 & 3 \\
+ 0 & -10 & -10 & 1 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccc}
+ 1 & 0 & 0 & 0 \\
+ 0 & 1 & 0 & 0 \\
+ 0 & 0 & 1 & 0 \\
+ 0 & 0 & 0 & 1 \\
+ 0 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 0 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/36785.txt

@@ -0,0 +1,19 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccccc}
+ -1 & 0 & -6 & 5 & 6 & -7 \\
+ 6 & 7 & -3 & 0 & 9 & -5 \\
+ 9 & 7 & -7 & 9 & 9 & -7 \\
+ -1 & 10 & -7 & -1 & 6 & 2 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccccc}
+ 1 & 0 & 0 & 0 & \frac{471}{278} & -\frac{3295}{1668} \\
+ 0 & 1 & 0 & 0 & -\frac{189}{139} & \frac{312}{139} \\
+ 0 & 0 & 1 & 0 & -\frac{387}{139} & \frac{821}{278} \\
+ 0 & 0 & 0 & 1 & -\frac{501}{278} & \frac{2917}{1668} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/39016.txt

@@ -0,0 +1,25 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cc}
+ -8 & 8 \\
+ -7 & -2 \\
+ 9 & -6 \\
+ 6 & 0 \\
+ -9 & -6 \\
+ 3 & 3 \\
+ -7 & -9 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cc}
+ 1 & 0 \\
+ 0 & 1 \\
+ 0 & 0 \\
+ 0 & 0 \\
+ 0 & 0 \\
+ 0 & 0 \\
+ 0 & 0 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/39127.txt

@@ -0,0 +1,15 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{ccccccc}
+ 7 & -10 & 1 & 9 & 1 & 1 & -7 \\
+ 4 & -9 & -2 & 7 & -6 & 7 & 4 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{ccccccc}
+ 1 & 0 & \frac{29}{23} & \frac{11}{23} & 3 & -\frac{61}{23} & -\frac{103}{23} \\
+ 0 & 1 & \frac{18}{23} & -\frac{13}{23} & 2 & -\frac{45}{23} & -\frac{56}{23} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/39328.txt

@@ -0,0 +1,23 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccc}
+ -2 & -2 & 2 & -1 \\
+ 4 & -5 & -6 & 3 \\
+ -10 & -7 & 8 & 10 \\
+ 0 & 10 & 1 & -2 \\
+ 6 & -4 & -2 & -2 \\
+ -6 & 6 & -10 & -5 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccc}
+ 1 & 0 & 0 & 0 \\
+ 0 & 1 & 0 & 0 \\
+ 0 & 0 & 1 & 0 \\
+ 0 & 0 & 0 & 1 \\
+ 0 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 0 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/3993.txt

@@ -0,0 +1,21 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccccc}
+ 0 & -4 & 6 & 5 & -1 & -9 \\
+ 9 & -3 & 8 & 10 & -5 & -3 \\
+ 8 & 10 & -3 & -3 & 6 & 7 \\
+ 6 & -8 & -4 & -4 & 8 & 6 \\
+ -4 & -8 & 0 & -5 & -2 & -4 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccccc}
+ 1 & 0 & 0 & 0 & 0 & \frac{4949}{7703} \\
+ 0 & 1 & 0 & 0 & 0 & \frac{121}{7703} \\
+ 0 & 0 & 1 & 0 & 0 & -\frac{14929}{7703} \\
+ 0 & 0 & 0 & 1 & 0 & \frac{3434}{7703} \\
+ 0 & 0 & 0 & 0 & 1 & -\frac{3561}{7703} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/40343.txt

@@ -0,0 +1,23 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccccc}
+ -9 & -9 & 4 & 8 & -2 & -10 \\
+ 1 & -7 & 7 & -3 & -6 & 7 \\
+ 1 & 4 & 10 & 6 & -9 & -3 \\
+ 8 & 2 & -4 & -6 & -9 & -6 \\
+ 7 & -7 & -5 & 3 & 2 & 7 \\
+ 1 & 10 & -6 & -3 & 0 & -9 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccccc}
+ 1 & 0 & 0 & 0 & 0 & 0 \\
+ 0 & 1 & 0 & 0 & 0 & 0 \\
+ 0 & 0 & 1 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 1 & 0 & 0 \\
+ 0 & 0 & 0 & 0 & 1 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 1 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/41334.txt

@@ -0,0 +1,21 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{ccccccc}
+ 1 & 6 & -3 & 0 & 7 & -9 & 5 \\
+ 2 & -6 & -6 & -9 & -4 & 8 & -10 \\
+ -10 & -10 & -4 & 0 & 4 & 8 & -8 \\
+ 1 & 4 & 1 & -1 & -1 & 8 & 4 \\
+ -4 & 10 & 7 & 8 & 1 & 8 & 2 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{ccccccc}
+ 1 & 0 & 0 & 0 & 0 & -\frac{401}{139} & \frac{119}{139} \\
+ 0 & 1 & 0 & 0 & 0 & \frac{761}{1251} & -\frac{1403}{1251} \\
+ 0 & 0 & 1 & 0 & 0 & \frac{10055}{2502} & \frac{18463}{2502} \\
+ 0 & 0 & 0 & 1 & 0 & -\frac{1985}{417} & -\frac{2071}{417} \\
+ 0 & 0 & 0 & 0 & 1 & \frac{91}{278} & \frac{1311}{278} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/41445.txt

@@ -0,0 +1,21 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{ccccccc}
+ 1 & -5 & 5 & 5 & 0 & 4 & 1 \\
+ 4 & 1 & 0 & -9 & -5 & -2 & 9 \\
+ -2 & 9 & 9 & -7 & 5 & -6 & -4 \\
+ -7 & 3 & -4 & 0 & -10 & -5 & 7 \\
+ 1 & -9 & -10 & -10 & 7 & 3 & -3 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{ccccccc}
+ 1 & 0 & 0 & 0 & 0 & \frac{53818}{165317} & \frac{39777}{165317} \\
+ 0 & 1 & 0 & 0 & 0 & -\frac{79653}{165317} & -\frac{48314}{165317} \\
+ 0 & 0 & 1 & 0 & 0 & \frac{1430}{165317} & \frac{34355}{165317} \\
+ 0 & 0 & 0 & 1 & 0 & \frac{40407}{165317} & -\frac{57561}{165317} \\
+ 0 & 0 & 0 & 0 & 1 & \frac{20518}{165317} & -\frac{171802}{165317} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/row_reduce/41550.txt

@@ -0,0 +1,19 @@
+Problem:
+Convert the following matrix to reduced row echelon form:
+$\left(
+\begin{array}{cccc}
+ 2 & -3 & -5 & 8 \\
+ -10 & -3 & 5 & -7 \\
+ 6 & -5 & -10 & 9 \\
+ 4 & 3 & 0 & 4 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccc}
+ 1 & 0 & 0 & 0 \\
+ 0 & 1 & 0 & 0 \\
+ 0 & 0 & 1 & 0 \\
+ 0 & 0 & 0 & 1 \\
+\end{array}
+\right)$