diff --git a/pretraining/mathematica/linear_algebra/row_reduce/10257.txt b/pretraining/mathematica/linear_algebra/row_reduce/10257.txt new file mode 100644 index 0000000000000000000000000000000000000000..b8e75722071357fd7d5acfa60b65af8d3c600f1c --- /dev/null +++ b/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: +$\left( +\begin{array}{ccccc} + 1 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 0 & 1 \\ + 0 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/10437.txt b/pretraining/mathematica/linear_algebra/row_reduce/10437.txt new file mode 100644 index 0000000000000000000000000000000000000000..95cca702e100f141713f5d6b5ec40966c979643f --- /dev/null +++ b/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: +$\left( +\begin{array}{ccccccc} + 1 & 0 & 0 & 0 & 0 & \frac{13227}{5627} & \frac{10094}{5627} \\ + 0 & 1 & 0 & 0 & 0 & -\frac{138375}{22508} & -\frac{51707}{11254} \\ + 0 & 0 & 1 & 0 & 0 & \frac{77589}{22508} & \frac{27589}{11254} \\ + 0 & 0 & 0 & 1 & 0 & -\frac{5963}{11254} & -\frac{1929}{5627} \\ + 0 & 0 & 0 & 0 & 1 & -\frac{21925}{5627} & -\frac{12498}{5627} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/11114.txt b/pretraining/mathematica/linear_algebra/row_reduce/11114.txt new file mode 100644 index 0000000000000000000000000000000000000000..0d62f6e4ba18190305e99261a2d4852c1583a06d --- /dev/null +++ b/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: +$\left( +\begin{array}{cc} + 1 & 0 \\ + 0 & 1 \\ + 0 & 0 \\ + 0 & 0 \\ + 0 & 0 \\ + 0 & 0 \\ + 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/11343.txt b/pretraining/mathematica/linear_algebra/row_reduce/11343.txt new file mode 100644 index 0000000000000000000000000000000000000000..d98e25ef27c9d688cecf4ecba8d2a141e3f4e52d --- /dev/null +++ b/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: +$\left( +\begin{array}{cccc} + 1 & 0 & \frac{59}{7} & -\frac{111}{7} \\ + 0 & 1 & 8 & -15 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/1163.txt b/pretraining/mathematica/linear_algebra/row_reduce/1163.txt new file mode 100644 index 0000000000000000000000000000000000000000..4b6ff0feb3e4c2b4f9a007e138d4a478c4751c33 --- /dev/null +++ b/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: +$\left( +\begin{array}{cccccc} + 1 & 0 & 0 & -\frac{1173}{91} & \frac{1024}{91} & -12 \\ + 0 & 1 & 0 & \frac{1299}{91} & -\frac{1080}{91} & 13 \\ + 0 & 0 & 1 & -\frac{248}{91} & \frac{194}{91} & -3 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/12477.txt b/pretraining/mathematica/linear_algebra/row_reduce/12477.txt new file mode 100644 index 0000000000000000000000000000000000000000..195d39be499188833e6f9d04fd9037bd38c66b0c --- /dev/null +++ b/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: +$\left( +\begin{array}{cccccc} + 1 & 0 & 0 & -\frac{474}{217} & \frac{333}{217} & \frac{6}{31} \\ + 0 & 1 & 0 & -\frac{428}{217} & \frac{243}{217} & \frac{27}{31} \\ + 0 & 0 & 1 & \frac{10}{31} & \frac{2}{31} & \frac{5}{31} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/12672.txt b/pretraining/mathematica/linear_algebra/row_reduce/12672.txt new file mode 100644 index 0000000000000000000000000000000000000000..6870115d439e967aa97a42dd22184ff488940e86 --- /dev/null +++ b/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: +$\left( +\begin{array}{cccccc} + 1 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 0 & 0 & 1 \\ + 0 & 0 & 0 & 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/14842.txt b/pretraining/mathematica/linear_algebra/row_reduce/14842.txt new file mode 100644 index 0000000000000000000000000000000000000000..ded8998cc57ccf5e9401df8acd6bd540b57894cc --- /dev/null +++ b/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: +$\left( +\begin{array}{ccccccc} + 1 & 0 & 0 & 0 & \frac{527}{2553} & \frac{13327}{7659} & -\frac{13090}{7659} \\ + 0 & 1 & 0 & 0 & -\frac{401}{851} & \frac{55}{851} & \frac{639}{851} \\ + 0 & 0 & 1 & 0 & \frac{2387}{2553} & -\frac{8117}{7659} & \frac{9641}{7659} \\ + 0 & 0 & 0 & 1 & \frac{50}{2553} & -\frac{6506}{7659} & \frac{1064}{7659} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/15771.txt b/pretraining/mathematica/linear_algebra/row_reduce/15771.txt new file mode 100644 index 0000000000000000000000000000000000000000..a60bd045222ae24fddadaac1b56704d08dbc425d --- /dev/null +++ b/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: +$\left( +\begin{array}{cccccc} + 1 & 0 & -\frac{3}{4} & -\frac{17}{2} & \frac{13}{4} & -\frac{35}{2} \\ + 0 & 1 & \frac{1}{2} & -9 & \frac{5}{2} & -15 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/18261.txt b/pretraining/mathematica/linear_algebra/row_reduce/18261.txt new file mode 100644 index 0000000000000000000000000000000000000000..c719550a03e9ba8d632899e5fffe6b2288c8a47c --- /dev/null +++ b/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: +$\left( +\begin{array}{cccccc} + 1 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 0 & 0 & 1 \\ + 0 & 0 & 0 & 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/18471.txt b/pretraining/mathematica/linear_algebra/row_reduce/18471.txt new file mode 100644 index 0000000000000000000000000000000000000000..c85124fb40da5c815e28dfeed4e070baf4080ed2 --- /dev/null +++ b/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: +$\left( +\begin{array}{cc} + 1 & 0 \\ + 0 & 1 \\ + 0 & 0 \\ + 0 & 0 \\ + 0 & 0 \\ + 0 & 0 \\ + 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/18665.txt b/pretraining/mathematica/linear_algebra/row_reduce/18665.txt new file mode 100644 index 0000000000000000000000000000000000000000..961b4eb511563564f70ae13712d7cb7c3d7d3d94 --- /dev/null +++ b/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: +$\left( +\begin{array}{cccccc} + 1 & 0 & 0 & \frac{3}{13} & -\frac{3}{13} & \frac{5}{13} \\ + 0 & 1 & -\frac{5}{2} & -\frac{115}{52} & \frac{63}{52} & -\frac{23}{13} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/19349.txt b/pretraining/mathematica/linear_algebra/row_reduce/19349.txt new file mode 100644 index 0000000000000000000000000000000000000000..cc806c970b7a3df570fffd50b74aa20f89042440 --- /dev/null +++ b/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: +$\left( +\begin{array}{ccccccc} + 1 & 0 & 0 & 0 & 0 & 0 & \frac{16261}{14461} \\ + 0 & 1 & 0 & 0 & 0 & 0 & -\frac{1208}{101227} \\ + 0 & 0 & 1 & 0 & 0 & 0 & \frac{62819}{101227} \\ + 0 & 0 & 0 & 1 & 0 & 0 & \frac{92434}{101227} \\ + 0 & 0 & 0 & 0 & 1 & 0 & \frac{58249}{101227} \\ + 0 & 0 & 0 & 0 & 0 & 1 & -\frac{62921}{101227} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/19633.txt b/pretraining/mathematica/linear_algebra/row_reduce/19633.txt new file mode 100644 index 0000000000000000000000000000000000000000..879646caa4cdb556fd0ca4be6896c1a525d49527 --- /dev/null +++ b/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: +$\left( +\begin{array}{ccccccc} + 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/20376.txt b/pretraining/mathematica/linear_algebra/row_reduce/20376.txt new file mode 100644 index 0000000000000000000000000000000000000000..8c62266706d42d040c408d30bb7eddc080a05371 --- /dev/null +++ b/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: +$\left( +\begin{array}{ccccc} + 1 & 0 & -\frac{44}{27} & \frac{83}{27} & -\frac{16}{27} \\ + 0 & 1 & \frac{16}{27} & -\frac{40}{27} & \frac{23}{27} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/20580.txt b/pretraining/mathematica/linear_algebra/row_reduce/20580.txt new file mode 100644 index 0000000000000000000000000000000000000000..4d3dcd0cd6c4f29db84a0713f395332275a76491 --- /dev/null +++ b/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: +$\left( +\begin{array}{cccc} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 1 \\ + 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/20645.txt b/pretraining/mathematica/linear_algebra/row_reduce/20645.txt new file mode 100644 index 0000000000000000000000000000000000000000..34c2aef5cfdae59c0944dc1f6b4da572707eee67 --- /dev/null +++ b/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: +$\left( +\begin{array}{cccccc} + 1 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 0 & 0 & 1 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/2109.txt b/pretraining/mathematica/linear_algebra/row_reduce/2109.txt new file mode 100644 index 0000000000000000000000000000000000000000..27c84b9f254b4089442193923afafd4f232ae70d --- /dev/null +++ b/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: +$\left( +\begin{array}{cc} + 1 & 0 \\ + 0 & 1 \\ + 0 & 0 \\ + 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/21464.txt b/pretraining/mathematica/linear_algebra/row_reduce/21464.txt new file mode 100644 index 0000000000000000000000000000000000000000..ea2d6ce809452f08c57db3d4c92f0e64f3252882 --- /dev/null +++ b/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: +$\left( +\begin{array}{cccccc} + 1 & 0 & \frac{8}{3} & -\frac{7}{3} & -1 & 1 \\ + 0 & 1 & -\frac{38}{9} & \frac{65}{18} & 1 & -\frac{7}{6} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/21500.txt b/pretraining/mathematica/linear_algebra/row_reduce/21500.txt new file mode 100644 index 0000000000000000000000000000000000000000..7a64f00735fe23c0b56c90c83d96017a2d263616 --- /dev/null +++ b/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: +$\left( +\begin{array}{cc} + 1 & 0 \\ + 0 & 1 \\ + 0 & 0 \\ + 0 & 0 \\ + 0 & 0 \\ + 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/21582.txt b/pretraining/mathematica/linear_algebra/row_reduce/21582.txt new file mode 100644 index 0000000000000000000000000000000000000000..ccb789b047d11e9a1f8eea06a632b74a6a0df602 --- /dev/null +++ b/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: +$\left( +\begin{array}{cc} + 1 & 0 \\ + 0 & 1 \\ + 0 & 0 \\ + 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/22247.txt b/pretraining/mathematica/linear_algebra/row_reduce/22247.txt new file mode 100644 index 0000000000000000000000000000000000000000..cba5f840973b581506d8d21cc5b2f014a878d544 --- /dev/null +++ b/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: +$\left( +\begin{array}{cccccc} + 1 & 0 & 0 & \frac{11}{16} & \frac{7}{16} & -\frac{13}{16} \\ + 0 & 1 & 0 & \frac{3}{80} & -\frac{141}{400} & -\frac{37}{80} \\ + 0 & 0 & 1 & -\frac{53}{40} & \frac{51}{200} & \frac{27}{40} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/23161.txt b/pretraining/mathematica/linear_algebra/row_reduce/23161.txt new file mode 100644 index 0000000000000000000000000000000000000000..b01a2e53b83b6567ac7188988e18cbc667cc5505 --- /dev/null +++ b/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: +$\left( +\begin{array}{ccccc} + 1 & 0 & 0 & \frac{135}{97} & -\frac{187}{97} \\ + 0 & 1 & 0 & \frac{75}{97} & \frac{47}{97} \\ + 0 & 0 & 1 & \frac{245}{97} & -\frac{131}{97} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/23329.txt b/pretraining/mathematica/linear_algebra/row_reduce/23329.txt new file mode 100644 index 0000000000000000000000000000000000000000..624bb69d74dd09ed04d740286cfca9264b481a88 --- /dev/null +++ b/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: +$\left( +\begin{array}{cc} + 1 & 0 \\ + 0 & 1 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/23684.txt b/pretraining/mathematica/linear_algebra/row_reduce/23684.txt new file mode 100644 index 0000000000000000000000000000000000000000..c1ab2d8ba5714c70b302cbe63578189f51a69b92 --- /dev/null +++ b/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: +$\left( +\begin{array}{ccccccc} + 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/23755.txt b/pretraining/mathematica/linear_algebra/row_reduce/23755.txt new file mode 100644 index 0000000000000000000000000000000000000000..70e5f0e246b7af9293f0e0786d639f27835ee26d --- /dev/null +++ b/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: +$\left( +\begin{array}{cccc} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 1 \\ + 0 & 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/23762.txt b/pretraining/mathematica/linear_algebra/row_reduce/23762.txt new file mode 100644 index 0000000000000000000000000000000000000000..885fffc24638d1c6b1dc009f926403ea5978acd0 --- /dev/null +++ b/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: +$\left( +\begin{array}{cccccc} + 1 & 0 & 0 & 0 & 0 & \frac{63369}{133198} \\ + 0 & 1 & 0 & 0 & 0 & -\frac{5435}{66599} \\ + 0 & 0 & 1 & 0 & 0 & -\frac{15649}{133198} \\ + 0 & 0 & 0 & 1 & 0 & \frac{6423}{10246} \\ + 0 & 0 & 0 & 0 & 1 & \frac{72687}{133198} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/24111.txt b/pretraining/mathematica/linear_algebra/row_reduce/24111.txt new file mode 100644 index 0000000000000000000000000000000000000000..358ad496823d7efb88064971355b7f88d6617312 --- /dev/null +++ b/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: +$\left( +\begin{array}{cccc} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 1 \\ + 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/26090.txt b/pretraining/mathematica/linear_algebra/row_reduce/26090.txt new file mode 100644 index 0000000000000000000000000000000000000000..5840c0e7800fe14804def4e0f662baf28bd08109 --- /dev/null +++ b/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: +$\left( +\begin{array}{cc} + 1 & 0 \\ + 0 & 1 \\ + 0 & 0 \\ + 0 & 0 \\ + 0 & 0 \\ + 0 & 0 \\ + 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/26166.txt b/pretraining/mathematica/linear_algebra/row_reduce/26166.txt new file mode 100644 index 0000000000000000000000000000000000000000..7817cfea83d23691dae82ca7348b8b8e8bfc5803 --- /dev/null +++ b/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: +$\left( +\begin{array}{ccc} + 1 & 0 & 0 \\ + 0 & 1 & 0 \\ + 0 & 0 & 1 \\ + 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/28340.txt b/pretraining/mathematica/linear_algebra/row_reduce/28340.txt new file mode 100644 index 0000000000000000000000000000000000000000..ecb3e36dfd50ae1f6f52bd8a2e6af1fc9706cb7b --- /dev/null +++ b/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: +$\left( +\begin{array}{ccccc} + 1 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 0 & 1 \\ + 0 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/2843.txt b/pretraining/mathematica/linear_algebra/row_reduce/2843.txt new file mode 100644 index 0000000000000000000000000000000000000000..35b2d9d028819b1489ba9e84a90851d03e918763 --- /dev/null +++ b/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: +$\left( +\begin{array}{cccccc} + 1 & 0 & -\frac{49}{46} & \frac{31}{46} & \frac{19}{23} & \frac{3}{23} \\ + 0 & 1 & \frac{5}{23} & -\frac{44}{23} & -\frac{48}{23} & -\frac{33}{23} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/29189.txt b/pretraining/mathematica/linear_algebra/row_reduce/29189.txt new file mode 100644 index 0000000000000000000000000000000000000000..f476ccf1462d3e559545da256890cff38520c251 --- /dev/null +++ b/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: +$\left( +\begin{array}{cc} + 1 & 0 \\ + 0 & 1 \\ + 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/29788.txt b/pretraining/mathematica/linear_algebra/row_reduce/29788.txt new file mode 100644 index 0000000000000000000000000000000000000000..14726cb5ed57981248646200a6573eb57de8be8e --- /dev/null +++ b/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: +$\left( +\begin{array}{cccc} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 1 \\ + 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/31029.txt b/pretraining/mathematica/linear_algebra/row_reduce/31029.txt new file mode 100644 index 0000000000000000000000000000000000000000..cbd08ed23fe09cd404f690925c1cc447269268fb --- /dev/null +++ b/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: +$\left( +\begin{array}{ccccc} + 1 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 0 & 1 \\ + 0 & 0 & 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/31174.txt b/pretraining/mathematica/linear_algebra/row_reduce/31174.txt new file mode 100644 index 0000000000000000000000000000000000000000..820afe003eef666e9668334d61a56e010f42ac3d --- /dev/null +++ b/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: +$\left( +\begin{array}{cccccc} + 1 & 0 & \frac{24}{31} & -\frac{34}{31} & -\frac{39}{31} & -\frac{26}{31} \\ + 0 & 1 & -\frac{61}{31} & -\frac{4}{31} & -\frac{21}{31} & \frac{17}{31} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/32566.txt b/pretraining/mathematica/linear_algebra/row_reduce/32566.txt new file mode 100644 index 0000000000000000000000000000000000000000..d75db4008b171c76dbb76c0cdb284f9074391e26 --- /dev/null +++ b/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: +$\left( +\begin{array}{ccccc} + 1 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 0 & 1 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/33479.txt b/pretraining/mathematica/linear_algebra/row_reduce/33479.txt new file mode 100644 index 0000000000000000000000000000000000000000..a66407623335a7ab8554a74781c7748149ee9d54 --- /dev/null +++ b/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: +$\left( +\begin{array}{ccc} + 1 & 0 & 0 \\ + 0 & 1 & 0 \\ + 0 & 0 & 1 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/34818.txt b/pretraining/mathematica/linear_algebra/row_reduce/34818.txt new file mode 100644 index 0000000000000000000000000000000000000000..100fb8d1944f7bce776c497ae74a8349ecadd557 --- /dev/null +++ b/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: +$\left( +\begin{array}{ccccc} + 1 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 0 & 1 \\ + 0 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/34931.txt b/pretraining/mathematica/linear_algebra/row_reduce/34931.txt new file mode 100644 index 0000000000000000000000000000000000000000..67de1cbcc519b83ed2784705e1f6a8f3ed9d68c7 --- /dev/null +++ b/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: +$\left( +\begin{array}{cc} + 1 & 0 \\ + 0 & 1 \\ + 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/36564.txt b/pretraining/mathematica/linear_algebra/row_reduce/36564.txt new file mode 100644 index 0000000000000000000000000000000000000000..62f277df7036f4974706800a7d93624f38453ec7 --- /dev/null +++ b/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: +$\left( +\begin{array}{cccc} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 1 \\ + 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/36785.txt b/pretraining/mathematica/linear_algebra/row_reduce/36785.txt new file mode 100644 index 0000000000000000000000000000000000000000..dc02ccadb4cdfe412f94fecf37721a1d30eba648 --- /dev/null +++ b/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: +$\left( +\begin{array}{cccccc} + 1 & 0 & 0 & 0 & \frac{471}{278} & -\frac{3295}{1668} \\ + 0 & 1 & 0 & 0 & -\frac{189}{139} & \frac{312}{139} \\ + 0 & 0 & 1 & 0 & -\frac{387}{139} & \frac{821}{278} \\ + 0 & 0 & 0 & 1 & -\frac{501}{278} & \frac{2917}{1668} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/39016.txt b/pretraining/mathematica/linear_algebra/row_reduce/39016.txt new file mode 100644 index 0000000000000000000000000000000000000000..c1216c5aaa601081cd5cf562766f67088880714e --- /dev/null +++ b/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: +$\left( +\begin{array}{cc} + 1 & 0 \\ + 0 & 1 \\ + 0 & 0 \\ + 0 & 0 \\ + 0 & 0 \\ + 0 & 0 \\ + 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/39127.txt b/pretraining/mathematica/linear_algebra/row_reduce/39127.txt new file mode 100644 index 0000000000000000000000000000000000000000..4fe0ce6d47bda4b2f50ad44cd3135b8e60beb5b1 --- /dev/null +++ b/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: +$\left( +\begin{array}{ccccccc} + 1 & 0 & \frac{29}{23} & \frac{11}{23} & 3 & -\frac{61}{23} & -\frac{103}{23} \\ + 0 & 1 & \frac{18}{23} & -\frac{13}{23} & 2 & -\frac{45}{23} & -\frac{56}{23} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/39328.txt b/pretraining/mathematica/linear_algebra/row_reduce/39328.txt new file mode 100644 index 0000000000000000000000000000000000000000..d63baf8a54f73fcdfa90499c7f38f5fda2b95823 --- /dev/null +++ b/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: +$\left( +\begin{array}{cccc} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 1 \\ + 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/3993.txt b/pretraining/mathematica/linear_algebra/row_reduce/3993.txt new file mode 100644 index 0000000000000000000000000000000000000000..1e7393e415d7fd4b93b429000f0f0ef15a6fecc2 --- /dev/null +++ b/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: +$\left( +\begin{array}{cccccc} + 1 & 0 & 0 & 0 & 0 & \frac{4949}{7703} \\ + 0 & 1 & 0 & 0 & 0 & \frac{121}{7703} \\ + 0 & 0 & 1 & 0 & 0 & -\frac{14929}{7703} \\ + 0 & 0 & 0 & 1 & 0 & \frac{3434}{7703} \\ + 0 & 0 & 0 & 0 & 1 & -\frac{3561}{7703} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/40343.txt b/pretraining/mathematica/linear_algebra/row_reduce/40343.txt new file mode 100644 index 0000000000000000000000000000000000000000..2f9e3a2d672ca40de3d3682389335d3b9f85285f --- /dev/null +++ b/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: +$\left( +\begin{array}{cccccc} + 1 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 0 & 0 & 1 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/41334.txt b/pretraining/mathematica/linear_algebra/row_reduce/41334.txt new file mode 100644 index 0000000000000000000000000000000000000000..0639d15f8c78a51ba3ab3437e362c0c49c0ae966 --- /dev/null +++ b/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: +$\left( +\begin{array}{ccccccc} + 1 & 0 & 0 & 0 & 0 & -\frac{401}{139} & \frac{119}{139} \\ + 0 & 1 & 0 & 0 & 0 & \frac{761}{1251} & -\frac{1403}{1251} \\ + 0 & 0 & 1 & 0 & 0 & \frac{10055}{2502} & \frac{18463}{2502} \\ + 0 & 0 & 0 & 1 & 0 & -\frac{1985}{417} & -\frac{2071}{417} \\ + 0 & 0 & 0 & 0 & 1 & \frac{91}{278} & \frac{1311}{278} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/41445.txt b/pretraining/mathematica/linear_algebra/row_reduce/41445.txt new file mode 100644 index 0000000000000000000000000000000000000000..89f6f6746a66622578b68b6cc7aa6baec33d7cb6 --- /dev/null +++ b/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: +$\left( +\begin{array}{ccccccc} + 1 & 0 & 0 & 0 & 0 & \frac{53818}{165317} & \frac{39777}{165317} \\ + 0 & 1 & 0 & 0 & 0 & -\frac{79653}{165317} & -\frac{48314}{165317} \\ + 0 & 0 & 1 & 0 & 0 & \frac{1430}{165317} & \frac{34355}{165317} \\ + 0 & 0 & 0 & 1 & 0 & \frac{40407}{165317} & -\frac{57561}{165317} \\ + 0 & 0 & 0 & 0 & 1 & \frac{20518}{165317} & -\frac{171802}{165317} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/41550.txt b/pretraining/mathematica/linear_algebra/row_reduce/41550.txt new file mode 100644 index 0000000000000000000000000000000000000000..bf709c832c68795b0f7663671ec003620f1ca110 --- /dev/null +++ b/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: +$\left( +\begin{array}{cccc} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 1 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/41887.txt b/pretraining/mathematica/linear_algebra/row_reduce/41887.txt new file mode 100644 index 0000000000000000000000000000000000000000..a724cfe858cee25a1932097cd66dc4e0da2c26df --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/41887.txt @@ -0,0 +1,25 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{cccc} + 8 & -8 & 4 & -2 \\ + -7 & 9 & -6 & 1 \\ + -9 & -1 & -9 & 10 \\ + 10 & -4 & -1 & -5 \\ + -2 & -4 & 1 & 1 \\ + -4 & 6 & 7 & 6 \\ + 9 & 0 & -7 & 8 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{cccc} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 1 \\ + 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/43444.txt b/pretraining/mathematica/linear_algebra/row_reduce/43444.txt new file mode 100644 index 0000000000000000000000000000000000000000..92fb5a9bac971e651cc7e312b6ff83cf0906d7f6 --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/43444.txt @@ -0,0 +1,15 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{cccccc} + 4 & 9 & 3 & 3 & 0 & -2 \\ + -1 & 6 & -2 & 10 & -3 & -7 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{cccccc} + 1 & 0 & \frac{12}{11} & -\frac{24}{11} & \frac{9}{11} & \frac{17}{11} \\ + 0 & 1 & -\frac{5}{33} & \frac{43}{33} & -\frac{4}{11} & -\frac{10}{11} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/43731.txt b/pretraining/mathematica/linear_algebra/row_reduce/43731.txt new file mode 100644 index 0000000000000000000000000000000000000000..a94f61adfd292b391fa1e54d8b36ac4fed3966f3 --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/43731.txt @@ -0,0 +1,23 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{ccccccc} + -10 & 9 & 1 & -7 & 6 & 9 & -5 \\ + -8 & 1 & 9 & -1 & 6 & 1 & -7 \\ + 2 & -8 & -10 & 3 & -1 & 1 & -8 \\ + 3 & 3 & 2 & 9 & 4 & 5 & 1 \\ + -3 & -3 & -7 & 5 & -1 & 8 & 1 \\ + 4 & -5 & -6 & -10 & -5 & 4 & 1 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{ccccccc} + 1 & 0 & 0 & 0 & 0 & 0 & \frac{13747}{249900} \\ + 0 & 1 & 0 & 0 & 0 & 0 & \frac{124291}{166600} \\ + 0 & 0 & 1 & 0 & 0 & 0 & \frac{29549}{49980} \\ + 0 & 0 & 0 & 1 & 0 & 0 & \frac{34569}{83300} \\ + 0 & 0 & 0 & 0 & 1 & 0 & -\frac{350751}{166600} \\ + 0 & 0 & 0 & 0 & 0 & 1 & \frac{12353}{29400} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/44985.txt b/pretraining/mathematica/linear_algebra/row_reduce/44985.txt new file mode 100644 index 0000000000000000000000000000000000000000..c8049b5c955c22b881a4f978ac652d9f87e74345 --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/44985.txt @@ -0,0 +1,25 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{ccc} + 9 & 7 & 0 \\ + 4 & -7 & -5 \\ + -1 & -6 & -3 \\ + 5 & -7 & 2 \\ + 10 & 3 & 9 \\ + 3 & -9 & 3 \\ + 9 & -7 & -6 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{ccc} + 1 & 0 & 0 \\ + 0 & 1 & 0 \\ + 0 & 0 & 1 \\ + 0 & 0 & 0 \\ + 0 & 0 & 0 \\ + 0 & 0 & 0 \\ + 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/45355.txt b/pretraining/mathematica/linear_algebra/row_reduce/45355.txt new file mode 100644 index 0000000000000000000000000000000000000000..28e7e0611468891034f11248e7b85b3378ced8ce --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/45355.txt @@ -0,0 +1,25 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{ccccc} + -6 & -7 & 0 & -6 & 2 \\ + -2 & 7 & 6 & -7 & -6 \\ + -10 & 8 & 5 & 4 & -6 \\ + -6 & 2 & -9 & 3 & -1 \\ + -9 & 1 & -3 & -2 & -5 \\ + 6 & 7 & 1 & 8 & -7 \\ + 9 & 3 & -4 & -7 & 10 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{ccccc} + 1 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 0 & 1 \\ + 0 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/45522.txt b/pretraining/mathematica/linear_algebra/row_reduce/45522.txt new file mode 100644 index 0000000000000000000000000000000000000000..2dc4563970248a72c80efb43b3b140351b5cd505 --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/45522.txt @@ -0,0 +1,21 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{ccc} + 8 & 1 & 2 \\ + -6 & -3 & -3 \\ + 8 & -7 & -9 \\ + 4 & -4 & 8 \\ + 5 & -9 & -5 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{ccc} + 1 & 0 & 0 \\ + 0 & 1 & 0 \\ + 0 & 0 & 1 \\ + 0 & 0 & 0 \\ + 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/47405.txt b/pretraining/mathematica/linear_algebra/row_reduce/47405.txt new file mode 100644 index 0000000000000000000000000000000000000000..86837591abcac3590c1b25f248ef41d5ac2b777a --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/47405.txt @@ -0,0 +1,17 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{cc} + -5 & 0 \\ + 7 & 2 \\ + 2 & -7 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{cc} + 1 & 0 \\ + 0 & 1 \\ + 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/47465.txt b/pretraining/mathematica/linear_algebra/row_reduce/47465.txt new file mode 100644 index 0000000000000000000000000000000000000000..6aa1787e1c1e6bae0d43752ba3dcf06d17ee8157 --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/47465.txt @@ -0,0 +1,15 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{ccccccc} + 9 & 10 & -10 & 3 & 3 & 8 & 6 \\ + 6 & -9 & -2 & 5 & 5 & 5 & 6 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{ccccccc} + 1 & 0 & -\frac{110}{141} & \frac{77}{141} & \frac{77}{141} & \frac{122}{141} & \frac{38}{47} \\ + 0 & 1 & -\frac{14}{47} & -\frac{9}{47} & -\frac{9}{47} & \frac{1}{47} & -\frac{6}{47} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/47682.txt b/pretraining/mathematica/linear_algebra/row_reduce/47682.txt new file mode 100644 index 0000000000000000000000000000000000000000..b9bef621cfeb408262af2b91b45245e30f772afa --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/47682.txt @@ -0,0 +1,23 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{cccccc} + 4 & -3 & 8 & 9 & 0 & -5 \\ + -9 & -10 & 0 & 4 & 4 & 8 \\ + -8 & 2 & 8 & 2 & 10 & -8 \\ + 3 & -1 & -10 & -1 & -9 & 3 \\ + 5 & 10 & 2 & 10 & -5 & -2 \\ + -1 & 5 & 6 & 5 & 9 & 0 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{cccccc} + 1 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 0 & 0 & 1 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/47950.txt b/pretraining/mathematica/linear_algebra/row_reduce/47950.txt new file mode 100644 index 0000000000000000000000000000000000000000..6629bddf9d6a59d086eace00ebcf9438cc5ed143 --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/47950.txt @@ -0,0 +1,19 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{ccc} + 2 & 4 & 5 \\ + 7 & -4 & -8 \\ + -7 & -3 & 8 \\ + -7 & -3 & 9 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{ccc} + 1 & 0 & 0 \\ + 0 & 1 & 0 \\ + 0 & 0 & 1 \\ + 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/48280.txt b/pretraining/mathematica/linear_algebra/row_reduce/48280.txt new file mode 100644 index 0000000000000000000000000000000000000000..9d2be6f0594e88d9e1e76cb9cdb4c4efe46dcc79 --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/48280.txt @@ -0,0 +1,15 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{ccccccc} + -3 & -1 & -10 & -5 & 7 & 9 & 3 \\ + 3 & 4 & 3 & -4 & -9 & -4 & -10 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{ccccccc} + 1 & 0 & \frac{37}{9} & \frac{8}{3} & -\frac{19}{9} & -\frac{32}{9} & -\frac{2}{9} \\ + 0 & 1 & -\frac{7}{3} & -3 & -\frac{2}{3} & \frac{5}{3} & -\frac{7}{3} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/49336.txt b/pretraining/mathematica/linear_algebra/row_reduce/49336.txt new file mode 100644 index 0000000000000000000000000000000000000000..a3adc18156ddc73e722c583bc1f3f88f3a30bbd1 --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/49336.txt @@ -0,0 +1,19 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{ccccc} + 0 & -3 & 9 & -8 & 9 \\ + 4 & -10 & -4 & 8 & 3 \\ + -10 & 7 & 0 & 0 & 0 \\ + 8 & 3 & -6 & -5 & -8 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{ccccc} + 1 & 0 & 0 & 0 & -\frac{3997}{5296} \\ + 0 & 1 & 0 & 0 & -\frac{2855}{2648} \\ + 0 & 0 & 1 & 0 & \frac{531}{2648} \\ + 0 & 0 & 0 & 1 & -\frac{1311}{2648} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/49424.txt b/pretraining/mathematica/linear_algebra/row_reduce/49424.txt new file mode 100644 index 0000000000000000000000000000000000000000..9210db81978683d0d5be9ee0696894d4b089bed0 --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/49424.txt @@ -0,0 +1,23 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{ccccccc} + 5 & 7 & 8 & 7 & -2 & 6 & 5 \\ + 3 & 1 & -2 & 3 & -2 & 6 & 10 \\ + 1 & 3 & 8 & -8 & -4 & -9 & 2 \\ + 0 & -7 & 2 & -5 & -6 & 8 & 2 \\ + 0 & -3 & -7 & 3 & -9 & 2 & -4 \\ + -9 & 6 & -10 & -6 & -10 & -10 & -7 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{ccccccc} + 1 & 0 & 0 & 0 & 0 & 0 & \frac{572559}{230512} \\ + 0 & 1 & 0 & 0 & 0 & 0 & \frac{589053}{461024} \\ + 0 & 0 & 1 & 0 & 0 & 0 & -\frac{490363}{461024} \\ + 0 & 0 & 0 & 1 & 0 & 0 & -\frac{806511}{461024} \\ + 0 & 0 & 0 & 0 & 1 & 0 & \frac{211779}{461024} \\ + 0 & 0 & 0 & 0 & 0 & 1 & \frac{408033}{461024} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/49754.txt b/pretraining/mathematica/linear_algebra/row_reduce/49754.txt new file mode 100644 index 0000000000000000000000000000000000000000..bd86333d9452f0fffb8a1a20cb9a1381e4f7a388 --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/49754.txt @@ -0,0 +1,19 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{ccc} + 2 & 1 & -6 \\ + -10 & 10 & -4 \\ + 0 & -1 & 2 \\ + -6 & -8 & -3 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{ccc} + 1 & 0 & 0 \\ + 0 & 1 & 0 \\ + 0 & 0 & 1 \\ + 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/49767.txt b/pretraining/mathematica/linear_algebra/row_reduce/49767.txt new file mode 100644 index 0000000000000000000000000000000000000000..324310a23e9bdfea038b43dc8525ebcd5fae9541 --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/49767.txt @@ -0,0 +1,23 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{ccccc} + -9 & -10 & -6 & 8 & 0 \\ + 10 & -4 & 6 & 6 & -9 \\ + 6 & 10 & 10 & 4 & 8 \\ + 0 & 0 & -8 & 0 & -5 \\ + 3 & -9 & 2 & 0 & -4 \\ + -6 & -1 & -10 & 4 & -10 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{ccccc} + 1 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 0 & 1 \\ + 0 & 0 & 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/6210.txt b/pretraining/mathematica/linear_algebra/row_reduce/6210.txt new file mode 100644 index 0000000000000000000000000000000000000000..20a6f5e703643da486d4a9f6989d5ef199fe399a --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/6210.txt @@ -0,0 +1,15 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{cc} + 9 & 1 \\ + -4 & 3 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{cc} + 1 & 0 \\ + 0 & 1 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/637.txt b/pretraining/mathematica/linear_algebra/row_reduce/637.txt new file mode 100644 index 0000000000000000000000000000000000000000..58556949d243355aee480281cb2be2a583dac90d --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/637.txt @@ -0,0 +1,19 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{cc} + -6 & -7 \\ + 8 & 5 \\ + -10 & 9 \\ + -4 & -5 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{cc} + 1 & 0 \\ + 0 & 1 \\ + 0 & 0 \\ + 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/6513.txt b/pretraining/mathematica/linear_algebra/row_reduce/6513.txt new file mode 100644 index 0000000000000000000000000000000000000000..b85a7cf6e65080fd4f598ffc9cbb9477ea1de34a --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/6513.txt @@ -0,0 +1,25 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{ccc} + -1 & -9 & 6 \\ + 2 & -3 & -5 \\ + -5 & 3 & 6 \\ + 9 & 4 & -2 \\ + -1 & 3 & -3 \\ + -4 & 2 & -5 \\ + 6 & 9 & -2 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{ccc} + 1 & 0 & 0 \\ + 0 & 1 & 0 \\ + 0 & 0 & 1 \\ + 0 & 0 & 0 \\ + 0 & 0 & 0 \\ + 0 & 0 & 0 \\ + 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/6999.txt b/pretraining/mathematica/linear_algebra/row_reduce/6999.txt new file mode 100644 index 0000000000000000000000000000000000000000..30e61732bbca54893918c8ad0a659534c23885ce --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/6999.txt @@ -0,0 +1,21 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{cc} + -3 & 1 \\ + 5 & 6 \\ + 5 & -8 \\ + 4 & 8 \\ + 1 & -6 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{cc} + 1 & 0 \\ + 0 & 1 \\ + 0 & 0 \\ + 0 & 0 \\ + 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/7236.txt b/pretraining/mathematica/linear_algebra/row_reduce/7236.txt new file mode 100644 index 0000000000000000000000000000000000000000..d4bd193f7088caffef7ca447edba3c6f69e47538 --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/7236.txt @@ -0,0 +1,25 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{ccccccc} + 7 & 5 & -9 & -8 & -6 & -5 & -2 \\ + 10 & -2 & -10 & 3 & 0 & 9 & 7 \\ + 0 & 9 & -5 & -6 & -9 & -1 & 6 \\ + 3 & 8 & -5 & -4 & 6 & -1 & 6 \\ + 6 & 1 & 4 & -4 & -7 & -8 & -10 \\ + 7 & -9 & -7 & -8 & 5 & 9 & 6 \\ + 2 & -6 & 10 & -4 & 0 & 6 & -6 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{ccccccc} + 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/7619.txt b/pretraining/mathematica/linear_algebra/row_reduce/7619.txt new file mode 100644 index 0000000000000000000000000000000000000000..db395d4c7e24a8d5db2400bbe85a8cc6e0010c59 --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/7619.txt @@ -0,0 +1,19 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{ccccc} + -4 & -3 & -4 & 6 & 7 \\ + -4 & 10 & -10 & 7 & 1 \\ + -8 & 10 & -2 & -1 & -4 \\ + 9 & 3 & 4 & -9 & 6 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{ccccc} + 1 & 0 & 0 & 0 & -\frac{923}{824} \\ + 0 & 1 & 0 & 0 & -\frac{699}{206} \\ + 0 & 0 & 1 & 0 & -\frac{12171}{1648} \\ + 0 & 0 & 0 & 1 & -\frac{5109}{824} \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/7915.txt b/pretraining/mathematica/linear_algebra/row_reduce/7915.txt new file mode 100644 index 0000000000000000000000000000000000000000..bacacbdf87dd6dfccdfbe30a40b10bf96ff6986e --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/7915.txt @@ -0,0 +1,19 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{cccc} + -3 & 8 & 7 & 4 \\ + 10 & -1 & -6 & -10 \\ + -7 & 2 & 8 & 2 \\ + -7 & -6 & 0 & -9 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{cccc} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 1 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/8044.txt b/pretraining/mathematica/linear_algebra/row_reduce/8044.txt new file mode 100644 index 0000000000000000000000000000000000000000..afba77b74d206ef0d25eb1f2ebad46d7dd21e20e --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/8044.txt @@ -0,0 +1,23 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{ccc} + 6 & -5 & 1 \\ + -8 & -6 & 8 \\ + 9 & -2 & 7 \\ + -7 & -8 & 3 \\ + -9 & 8 & -5 \\ + -4 & 7 & 4 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{ccc} + 1 & 0 & 0 \\ + 0 & 1 & 0 \\ + 0 & 0 & 1 \\ + 0 & 0 & 0 \\ + 0 & 0 & 0 \\ + 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/8050.txt b/pretraining/mathematica/linear_algebra/row_reduce/8050.txt new file mode 100644 index 0000000000000000000000000000000000000000..0d03d0e388aef7c907ed3a0fcf01371bf502a467 --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/8050.txt @@ -0,0 +1,25 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{ccc} + -3 & 9 & 1 \\ + -9 & 7 & 0 \\ + -6 & 3 & -9 \\ + -1 & -4 & 6 \\ + 8 & -5 & 7 \\ + -3 & -10 & 9 \\ + -3 & -7 & 2 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{ccc} + 1 & 0 & 0 \\ + 0 & 1 & 0 \\ + 0 & 0 & 1 \\ + 0 & 0 & 0 \\ + 0 & 0 & 0 \\ + 0 & 0 & 0 \\ + 0 & 0 & 0 \\ +\end{array} +\right)$ \ No newline at end of file diff --git a/pretraining/mathematica/linear_algebra/row_reduce/9207.txt b/pretraining/mathematica/linear_algebra/row_reduce/9207.txt new file mode 100644 index 0000000000000000000000000000000000000000..6acfe88fd3ea139e00d3aaab1e7dfa942a462a87 --- /dev/null +++ b/pretraining/mathematica/linear_algebra/row_reduce/9207.txt @@ -0,0 +1,17 @@ +Problem: +Convert the following matrix to reduced row echelon form: +$\left( +\begin{array}{cccc} + 0 & 6 & -6 & 8 \\ + -7 & -9 & -9 & 7 \\ + -1 & -9 & -8 & 0 \\ +\end{array} +\right)$. +Answer: +$\left( +\begin{array}{cccc} + 1 & 0 & 0 & -\frac{107}{101} \\ + 0 & 1 & 0 & \frac{209}{303} \\ + 0 & 0 & 1 & -\frac{65}{101} \\ +\end{array} +\right)$ \ No newline at end of file