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pretraining/mathematica/linear_algebra/null_space/10325.txt

@@ -0,0 +1,9 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccccc}
+ -10 & -2 & 8 & 6 & -8 \\
+\end{array}
+\right)$.
+Answer:
+${\{-4.,0.,0.,0.,5.\}, \{-1.,5.,0.,0.,0.\}, \{3.,0.,0.,5.,0.\}, \{4.,0.,5.,0.,0.\}}$

pretraining/mathematica/linear_algebra/null_space/10612.txt

@@ -0,0 +1,13 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccc}
+ -9 & 1 & 4 \\
+ -6 & -2 & 0 \\
+ -5 & 7 & -8 \\
+ -2 & -3 & 0 \\
+ 0 & 3 & -2 \\
+\end{array}
+\right)$.
+Answer:
+${}$

pretraining/mathematica/linear_algebra/null_space/1096.txt

@@ -0,0 +1,11 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccccc}
+ 2 & 8 & 4 & -4 & 1 \\
+ -5 & -5 & -3 & 0 & -2 \\
+ -2 & 8 & -4 & 0 & -10 \\
+\end{array}
+\right)$.
+Answer:
+${\{-22.,7.,25.,28.,0.\}, \{-22.,63.,-143.,0.,112.\}}$

pretraining/mathematica/linear_algebra/null_space/11590.txt

@@ -0,0 +1,9 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccc}
+ 0 & 8 & -3 \\
+\end{array}
+\right)$.
+Answer:
+${\{0.,3.,8.\}, \{1.,0.,0.\}}$

pretraining/mathematica/linear_algebra/null_space/12975.txt

@@ -0,0 +1,12 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccc}
+ -7 & 9 & 1 \\
+ 9 & -9 & 9 \\
+ 7 & 3 & 6 \\
+ -7 & 3 & -7 \\
+\end{array}
+\right)$.
+Answer:
+${}$

pretraining/mathematica/linear_algebra/null_space/13307.txt

@@ -0,0 +1,9 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{cccc}
+ -1 & 6 & -3 & -10 \\
+\end{array}
+\right)$.
+Answer:
+${\{-10.,0.,0.,1.\}, \{-3.,0.,1.,0.\}, \{6.,1.,0.,0.\}}$

pretraining/mathematica/linear_algebra/null_space/1332.txt

@@ -0,0 +1,13 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccccc}
+ 8 & 9 & 9 & 2 & -8 \\
+ 1 & 3 & -5 & -1 & 10 \\
+ -3 & -8 & 3 & -2 & 3 \\
+ 8 & 0 & -4 & 6 & -1 \\
+ -3 & 3 & 9 & 6 & -1 \\
+\end{array}
+\right)$.
+Answer:
+${}$

pretraining/mathematica/linear_algebra/null_space/13614.txt

@@ -0,0 +1,10 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccc}
+ 1 & -2 & 10 \\
+ -9 & 3 & 7 \\
+\end{array}
+\right)$.
+Answer:
+${\{44.,97.,15.\}}$

pretraining/mathematica/linear_algebra/null_space/13894.txt

@@ -0,0 +1,12 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccc}
+ 5 & -1 & -10 \\
+ -2 & -2 & 4 \\
+ 8 & 9 & 4 \\
+ 9 & -1 & -10 \\
+\end{array}
+\right)$.
+Answer:
+${}$

pretraining/mathematica/linear_algebra/null_space/14357.txt

@@ -0,0 +1,13 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccccc}
+ -9 & 6 & 5 & -10 & -3 \\
+ 8 & 3 & -9 & -2 & -5 \\
+ 3 & -6 & 1 & -6 & 10 \\
+ -9 & 1 & -9 & 3 & 2 \\
+ 8 & -10 & 9 & 6 & -10 \\
+\end{array}
+\right)$.
+Answer:
+${}$

pretraining/mathematica/linear_algebra/null_space/14617.txt

@@ -0,0 +1,12 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{cc}
+ 7 & -8 \\
+ -8 & 5 \\
+ -3 & 0 \\
+ -4 & 1 \\
+\end{array}
+\right)$.
+Answer:
+${}$

pretraining/mathematica/linear_algebra/null_space/14707.txt

@@ -0,0 +1,9 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{cccc}
+ -1 & -4 & -1 & -6 \\
+\end{array}
+\right)$.
+Answer:
+${\{-6.,0.,0.,1.\}, \{-4.,1.,0.,0.\}, \{-1.,0.,1.,0.\}}$

pretraining/mathematica/linear_algebra/null_space/14803.txt

@@ -0,0 +1,11 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{cccc}
+ -8 & 9 & 1 & -9 \\
+ -10 & -8 & -8 & -2 \\
+ -3 & 6 & -2 & -9 \\
+\end{array}
+\right)$.
+Answer:
+${\{-3.,37.,-42.,35.\}}$

pretraining/mathematica/linear_algebra/null_space/15026.txt

@@ -0,0 +1,12 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{cc}
+ -7 & -2 \\
+ -1 & 8 \\
+ 3 & 7 \\
+ 0 & -10 \\
+\end{array}
+\right)$.
+Answer:
+${}$

pretraining/mathematica/linear_algebra/null_space/15120.txt

@@ -0,0 +1,10 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccccc}
+ 0 & 8 & -3 & 6 & 4 \\
+ 8 & 4 & 9 & -1 & -9 \\
+\end{array}
+\right)$.
+Answer:
+${\{-21.,6.,16.,0.,0.\}, \{2.,-3.,0.,4.,0.\}, \{11.,-4.,0.,0.,8.\}}$

pretraining/mathematica/linear_algebra/null_space/16245.txt

@@ -0,0 +1,13 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{cc}
+ 7 & 9 \\
+ 4 & -9 \\
+ -9 & 0 \\
+ -1 & 6 \\
+ -5 & -8 \\
+\end{array}
+\right)$.
+Answer:
+${}$

pretraining/mathematica/linear_algebra/null_space/16736.txt

@@ -0,0 +1,9 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccccc}
+ -1 & 7 & 6 & 6 & -6 \\
+\end{array}
+\right)$.
+Answer:
+${\{-6.,0.,0.,0.,1.\}, \{6.,0.,0.,1.,0.\}, \{6.,0.,1.,0.,0.\}, \{7.,1.,0.,0.,0.\}}$

pretraining/mathematica/linear_algebra/null_space/17429.txt

@@ -0,0 +1,9 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccccc}
+ 4 & 6 & -10 & -3 & 2 \\
+\end{array}
+\right)$.
+Answer:
+${\{-3.,2.,0.,0.,0.\}, \{-1.,0.,0.,0.,2.\}, \{3.,0.,0.,4.,0.\}, \{5.,0.,2.,0.,0.\}}$

pretraining/mathematica/linear_algebra/null_space/17612.txt

@@ -0,0 +1,13 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccc}
+ -8 & -4 & 8 \\
+ -3 & -4 & -10 \\
+ 10 & 7 & 10 \\
+ -5 & -4 & 10 \\
+ -2 & 3 & -9 \\
+\end{array}
+\right)$.
+Answer:
+${}$

pretraining/mathematica/linear_algebra/null_space/17672.txt

@@ -0,0 +1,9 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{cccc}
+ -6 & -6 & -9 & 10 \\
+\end{array}
+\right)$.
+Answer:
+${\{-3.,0.,2.,0.\}, \{-1.,1.,0.,0.\}, \{5.,0.,0.,3.\}}$

pretraining/mathematica/linear_algebra/null_space/19249.txt

@@ -0,0 +1,12 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccccc}
+ 1 & 2 & 2 & -4 & -8 \\
+ 9 & 2 & -4 & -3 & -8 \\
+ 10 & 2 & 0 & 6 & 9 \\
+ 5 & -3 & -1 & 7 & 2 \\
+\end{array}
+\right)$.
+Answer:
+${\{1432.,-3599.,1471.,-2630.,962.\}}$

pretraining/mathematica/linear_algebra/null_space/20591.txt

@@ -0,0 +1,13 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{cccc}
+ 7 & 3 & 0 & -10 \\
+ 8 & 9 & 1 & 9 \\
+ 10 & -7 & 7 & 10 \\
+ -4 & -9 & 5 & 8 \\
+ 10 & -6 & -7 & 5 \\
+\end{array}
+\right)$.
+Answer:
+${}$

pretraining/mathematica/linear_algebra/null_space/22613.txt

@@ -0,0 +1,13 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccccc}
+ 4 & 5 & 3 & 4 & -1 \\
+ -7 & -5 & -6 & -9 & -2 \\
+ 3 & 10 & -8 & -9 & -6 \\
+ -4 & 6 & 9 & -3 & -3 \\
+ -10 & 3 & 0 & 8 & -5 \\
+\end{array}
+\right)$.
+Answer:
+${}$

pretraining/mathematica/linear_algebra/null_space/22718.txt

@@ -0,0 +1,10 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccc}
+ 3 & -6 & -5 \\
+ 2 & -1 & -4 \\
+\end{array}
+\right)$.
+Answer:
+${\{19.,2.,9.\}}$

pretraining/mathematica/linear_algebra/null_space/22971.txt

@@ -0,0 +1,13 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{cc}
+ -6 & -7 \\
+ -9 & -9 \\
+ 1 & 3 \\
+ -9 & 7 \\
+ 9 & -6 \\
+\end{array}
+\right)$.
+Answer:
+${}$

pretraining/mathematica/linear_algebra/null_space/23227.txt

@@ -0,0 +1,9 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccccc}
+ -6 & -4 & -10 & -7 & -2 \\
+\end{array}
+\right)$.
+Answer:
+${\{-7.,0.,0.,6.,0.\}, \{-5.,0.,3.,0.,0.\}, \{-2.,3.,0.,0.,0.\}, \{-1.,0.,0.,0.,3.\}}$

pretraining/mathematica/linear_algebra/null_space/2379.txt

@@ -0,0 +1,9 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccccc}
+ 1 & 6 & 2 & -4 & 2 \\
+\end{array}
+\right)$.
+Answer:
+${\{-6.,1.,0.,0.,0.\}, \{-2.,0.,0.,0.,1.\}, \{-2.,0.,1.,0.,0.\}, \{4.,0.,0.,1.,0.\}}$

pretraining/mathematica/linear_algebra/null_space/24041.txt

@@ -0,0 +1,10 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{cccc}
+ 4 & 2 & -7 & 6 \\
+ -8 & 1 & -5 & -7 \\
+\end{array}
+\right)$.
+Answer:
+${\{-3.,76.,20.,0.\}, \{-1.,-1.,0.,1.\}}$

pretraining/mathematica/linear_algebra/null_space/2483.txt

@@ -0,0 +1,10 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccccc}
+ 2 & -3 & 1 & -10 & -8 \\
+ -10 & -8 & -4 & -5 & 6 \\
+\end{array}
+\right)$.
+Answer:
+${\{-10.,1.,23.,0.,0.\}, \{41.,-34.,0.,0.,23.\}, \{65.,-110.,0.,46.,0.\}}$

pretraining/mathematica/linear_algebra/null_space/24980.txt

@@ -0,0 +1,13 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccc}
+ -3 & 9 & 5 \\
+ 4 & 6 & -3 \\
+ 9 & 9 & 0 \\
+ -5 & 7 & 6 \\
+ -4 & -10 & -10 \\
+\end{array}
+\right)$.
+Answer:
+${}$

pretraining/mathematica/linear_algebra/null_space/25017.txt

@@ -0,0 +1,12 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{cc}
+ -6 & -3 \\
+ 7 & -8 \\
+ -2 & -10 \\
+ 5 & 4 \\
+\end{array}
+\right)$.
+Answer:
+${}$

pretraining/mathematica/linear_algebra/null_space/25935.txt

@@ -0,0 +1,12 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccccc}
+ 9 & -6 & -7 & 2 & 7 \\
+ 3 & -2 & 3 & -1 & 10 \\
+ 1 & -5 & -1 & -9 & -7 \\
+ 10 & 8 & 9 & 5 & 5 \\
+\end{array}
+\right)$.
+Answer:
+${\{447.,14867.,-10394.,-10845.,4873.\}}$

pretraining/mathematica/linear_algebra/null_space/26297.txt

@@ -0,0 +1,12 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccc}
+ -5 & -5 & 5 \\
+ -7 & 0 & 2 \\
+ 8 & 9 & 0 \\
+ -7 & 7 & 3 \\
+\end{array}
+\right)$.
+Answer:
+${}$

pretraining/mathematica/linear_algebra/null_space/27649.txt

@@ -0,0 +1,10 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{cccc}
+ 7 & -9 & -10 & -1 \\
+ -5 & 10 & 6 & -10 \\
+\end{array}
+\right)$.
+Answer:
+${\{4.,3.,0.,1.\}, \{46.,8.,25.,0.\}}$

pretraining/mathematica/linear_algebra/null_space/27887.txt

@@ -0,0 +1,10 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccc}
+ 0 & 10 & -6 \\
+ 0 & -10 & -6 \\
+\end{array}
+\right)$.
+Answer:
+${\{1.,0.,0.\}}$

pretraining/mathematica/linear_algebra/null_space/28638.txt

@@ -0,0 +1,12 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccc}
+ 2 & 0 & 7 \\
+ 9 & 8 & -3 \\
+ 7 & 9 & 5 \\
+ 7 & 5 & -10 \\
+\end{array}
+\right)$.
+Answer:
+${}$

pretraining/mathematica/linear_algebra/null_space/28781.txt

@@ -0,0 +1,13 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccc}
+ 0 & 9 & 1 \\
+ 8 & -3 & -2 \\
+ 5 & 8 & 2 \\
+ -2 & 6 & 2 \\
+ -10 & -4 & 10 \\
+\end{array}
+\right)$.
+Answer:
+${}$

pretraining/mathematica/linear_algebra/null_space/29038.txt

@@ -0,0 +1,9 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{cc}
+ 8 & 6 \\
+\end{array}
+\right)$.
+Answer:
+${\{-3.,4.\}}$

pretraining/mathematica/linear_algebra/null_space/3060.txt

@@ -0,0 +1,13 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccccc}
+ -7 & -8 & 0 & 1 & -9 \\
+ -4 & 6 & -9 & 3 & -10 \\
+ 2 & 1 & 0 & 3 & 4 \\
+ -10 & 5 & 8 & -2 & -1 \\
+ 6 & -8 & 1 & -5 & -3 \\
+\end{array}
+\right)$.
+Answer:
+${}$

pretraining/mathematica/linear_algebra/null_space/30856.txt

@@ -0,0 +1,9 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{cccc}
+ -10 & 6 & 3 & -8 \\
+\end{array}
+\right)$.
+Answer:
+${\{-4.,0.,0.,5.\}, \{3.,0.,10.,0.\}, \{3.,5.,0.,0.\}}$

pretraining/mathematica/linear_algebra/null_space/30942.txt

@@ -0,0 +1,11 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{cccc}
+ 9 & 2 & -7 & -9 \\
+ 1 & 1 & -9 & -2 \\
+ 6 & -2 & 9 & 4 \\
+\end{array}
+\right)$.
+Answer:
+${\{45.,617.,40.,151.\}}$

pretraining/mathematica/linear_algebra/null_space/31569.txt

@@ -0,0 +1,12 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccc}
+ 6 & 7 & -8 \\
+ 5 & 3 & 5 \\
+ -7 & -10 & 10 \\
+ 7 & -2 & -7 \\
+\end{array}
+\right)$.
+Answer:
+${}$

pretraining/mathematica/linear_algebra/null_space/32117.txt

@@ -0,0 +1,12 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccccc}
+ 4 & 10 & -2 & 2 & 4 \\
+ -4 & -4 & 5 & 8 & 10 \\
+ -3 & -7 & 0 & -6 & -7 \\
+ 4 & 4 & 0 & 8 & -8 \\
+\end{array}
+\right)$.
+Answer:
+${\{-113.,-13.,-216.,67.,4.\}}$

pretraining/mathematica/linear_algebra/null_space/32256.txt

@@ -0,0 +1,13 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{cc}
+ -9 & -8 \\
+ 1 & -7 \\
+ -3 & -8 \\
+ 7 & -2 \\
+ 10 & 0 \\
+\end{array}
+\right)$.
+Answer:
+${}$

pretraining/mathematica/linear_algebra/null_space/32298.txt

@@ -0,0 +1,10 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{cccc}
+ 0 & -1 & 5 & 10 \\
+ -7 & -3 & 10 & -7 \\
+\end{array}
+\right)$.
+Answer:
+${\{-37.,70.,0.,7.\}, \{-5.,35.,7.,0.\}}$

pretraining/mathematica/linear_algebra/null_space/32485.txt

@@ -0,0 +1,11 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{cc}
+ 7 & -2 \\
+ 1 & 7 \\
+ 2 & -1 \\
+\end{array}
+\right)$.
+Answer:
+${}$

pretraining/mathematica/linear_algebra/null_space/33537.txt

@@ -0,0 +1,10 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccc}
+ -5 & 1 & -6 \\
+ -10 & 10 & 2 \\
+\end{array}
+\right)$.
+Answer:
+${\{-31.,-35.,20.\}}$

pretraining/mathematica/linear_algebra/null_space/34583.txt

@@ -0,0 +1,12 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccccc}
+ 4 & -7 & 4 & -5 & -8 \\
+ 1 & -9 & 8 & -7 & -8 \\
+ 1 & -3 & 2 & 7 & 3 \\
+ 8 & -9 & -3 & 1 & -7 \\
+\end{array}
+\right)$.
+Answer:
+${\{1084.,-431.,72.,-1051.,1612.\}}$

pretraining/mathematica/linear_algebra/null_space/35031.txt

@@ -0,0 +1,13 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccc}
+ 6 & -1 & -4 \\
+ 3 & -3 & -8 \\
+ 6 & -10 & -6 \\
+ 6 & -1 & 0 \\
+ -10 & -4 & 7 \\
+\end{array}
+\right)$.
+Answer:
+${}$

pretraining/mathematica/linear_algebra/null_space/35934.txt

@@ -0,0 +1,9 @@
+Problem:
+Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):
+$\left(
+\begin{array}{ccc}
+ -4 & -4 & 0 \\
+\end{array}
+\right)$.
+Answer:
+${\{-1.,1.,0.\}, \{0.,0.,1.\}}$