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pretraining/mathematica/linear_algebra/powers_and_exp/10298.txt

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+Problem:
+Compute
+$\left(
+\begin{array}{ccc}
+ -3 & -\frac{1}{2} & \frac{3}{2} \\
+ 1 & 1 & -2 \\
+ 3 & \frac{5}{2} & -\frac{1}{2} \\
+\end{array}
+\right)^2$.
+Answer:
+$\left(
+\begin{array}{ccc}
+ 13 & \frac{19}{4} & -\frac{17}{4} \\
+ -8 & -\frac{9}{2} & \frac{1}{2} \\
+ -8 & -\frac{1}{4} & -\frac{1}{4} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/powers_and_exp/10454.txt

@@ -0,0 +1,17 @@
+Problem:
+Compute
+$\left(
+\begin{array}{ccc}
+ 2 & 2 & 2 \\
+ 2 & 0 & -2 \\
+ 0 & -2 & -1 \\
+\end{array}
+\right)^2$.
+Answer:
+$\left(
+\begin{array}{ccc}
+ 8 & 0 & -2 \\
+ 4 & 8 & 6 \\
+ -4 & 2 & 5 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/powers_and_exp/10596.txt

@@ -0,0 +1,17 @@
+Problem:
+Compute
+$\left(
+\begin{array}{ccc}
+ -2 & -2 & 0 \\
+ 2 & -2 & 1 \\
+ -2 & -2 & -1 \\
+\end{array}
+\right)^3$.
+Answer:
+$\left(
+\begin{array}{ccc}
+ 20 & -12 & 10 \\
+ 22 & 30 & 1 \\
+ 18 & -22 & 11 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/powers_and_exp/21056.txt

@@ -0,0 +1,17 @@
+Problem:
+Compute
+$\left(
+\begin{array}{ccc}
+ -\frac{3}{2} & -\frac{1}{2} & \frac{1}{2} \\
+ -2 & -\frac{1}{2} & 3 \\
+ -\frac{3}{2} & -\frac{5}{2} & -1 \\
+\end{array}
+\right)^2$.
+Answer:
+$\left(
+\begin{array}{ccc}
+ \frac{5}{2} & -\frac{1}{4} & -\frac{11}{4} \\
+ -\frac{1}{2} & -\frac{25}{4} & -\frac{11}{2} \\
+ \frac{35}{4} & \frac{9}{2} & -\frac{29}{4} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/powers_and_exp/25022.txt

@@ -0,0 +1,15 @@
+Problem:
+Compute
+$\left(
+\begin{array}{cc}
+ -\frac{1}{2} & -2 \\
+ 2 & -\frac{3}{2} \\
+\end{array}
+\right)^2$.
+Answer:
+$\left(
+\begin{array}{cc}
+ -\frac{15}{4} & 4 \\
+ -4 & -\frac{7}{4} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/powers_and_exp/25393.txt

@@ -0,0 +1,15 @@
+Problem:
+Compute
+$\left(
+\begin{array}{cc}
+ -2 & 2 \\
+ 0 & 2 \\
+\end{array}
+\right)^2$.
+Answer:
+$\left(
+\begin{array}{cc}
+ 4 & 0 \\
+ 0 & 4 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/powers_and_exp/2774.txt

@@ -0,0 +1,17 @@
+Problem:
+Compute
+$\left(
+\begin{array}{ccc}
+ 2 & 2 & -3 \\
+ -1 & -2 & 1 \\
+ -1 & 0 & 2 \\
+\end{array}
+\right)^2$.
+Answer:
+$\left(
+\begin{array}{ccc}
+ 5 & 0 & -10 \\
+ -1 & 2 & 3 \\
+ -4 & -2 & 7 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/powers_and_exp/29929.txt

@@ -0,0 +1,17 @@
+Problem:
+Compute
+$\left(
+\begin{array}{ccc}
+ 1 & -\frac{5}{2} & \frac{5}{2} \\
+ -\frac{5}{2} & -\frac{3}{2} & \frac{3}{2} \\
+ \frac{5}{2} & -\frac{1}{2} & 1 \\
+\end{array}
+\right)^3$.
+Answer:
+$\left(
+\begin{array}{ccc}
+ \frac{133}{8} & -\frac{275}{8} & 35 \\
+ -\frac{255}{8} & -\frac{165}{8} & \frac{137}{8} \\
+ \frac{75}{2} & -\frac{79}{8} & \frac{105}{8} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/powers_and_exp/31018.txt

@@ -0,0 +1,15 @@
+Problem:
+Compute
+$\left(
+\begin{array}{cc}
+ 3 & -2 \\
+ 0 & -3 \\
+\end{array}
+\right)^3$.
+Answer:
+$\left(
+\begin{array}{cc}
+ 27 & -18 \\
+ 0 & -27 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/powers_and_exp/3336.txt

@@ -0,0 +1,17 @@
+Problem:
+Compute
+$\left(
+\begin{array}{ccc}
+ -\frac{3}{2} & -\frac{3}{2} & -\frac{5}{2} \\
+ -\frac{5}{2} & \frac{3}{2} & \frac{3}{2} \\
+ -\frac{3}{2} & -2 & 0 \\
+\end{array}
+\right)^3$.
+Answer:
+$\left(
+\begin{array}{ccc}
+ -\frac{235}{8} & -\frac{81}{8} & -\frac{135}{8} \\
+ -\frac{135}{8} & -\frac{73}{8} & \frac{81}{8} \\
+ -\frac{81}{8} & -\frac{27}{2} & -\frac{77}{4} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/powers_and_exp/33749.txt

@@ -0,0 +1,17 @@
+Problem:
+Compute
+$\left(
+\begin{array}{ccc}
+ 3 & \frac{1}{2} & 2 \\
+ 1 & -1 & 0 \\
+ 0 & \frac{3}{2} & \frac{1}{2} \\
+\end{array}
+\right)^3$.
+Answer:
+$\left(
+\begin{array}{ccc}
+ \frac{65}{2} & \frac{45}{4} & \frac{45}{2} \\
+ \frac{15}{2} & \frac{5}{2} & 5 \\
+ \frac{15}{4} & \frac{15}{8} & \frac{25}{8} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/powers_and_exp/34775.txt

@@ -0,0 +1,17 @@
+Problem:
+Compute
+$\left(
+\begin{array}{ccc}
+ 1 & 0 & -1 \\
+ 1 & -3 & -1 \\
+ 1 & -1 & -3 \\
+\end{array}
+\right)^3$.
+Answer:
+$\left(
+\begin{array}{ccc}
+ 3 & -5 & -7 \\
+ 12 & -35 & -22 \\
+ 12 & -27 & -30 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/powers_and_exp/36719.txt

@@ -0,0 +1,17 @@
+Problem:
+Compute
+$\left(
+\begin{array}{ccc}
+ -\frac{3}{2} & -1 & \frac{5}{2} \\
+ 0 & 2 & 2 \\
+ \frac{1}{2} & -\frac{1}{2} & -3 \\
+\end{array}
+\right)^3$.
+Answer:
+$\left(
+\begin{array}{ccc}
+ -\frac{95}{8} & -\frac{3}{8} & 45 \\
+ -\frac{5}{2} & 6 & \frac{29}{2} \\
+ 8 & -\frac{19}{8} & -\frac{267}{8} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/powers_and_exp/37272.txt

@@ -0,0 +1,15 @@
+Problem:
+Compute
+$\left(
+\begin{array}{cc}
+ -2 & -\frac{3}{2} \\
+ 2 & 1 \\
+\end{array}
+\right)^2$.
+Answer:
+$\left(
+\begin{array}{cc}
+ 1 & \frac{3}{2} \\
+ -2 & -2 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/powers_and_exp/37436.txt

@@ -0,0 +1,17 @@
+Problem:
+Compute
+$\left(
+\begin{array}{ccc}
+ -2 & \frac{5}{2} & \frac{3}{2} \\
+ -2 & -\frac{1}{2} & 1 \\
+ 2 & \frac{3}{2} & \frac{1}{2} \\
+\end{array}
+\right)^2$.
+Answer:
+$\left(
+\begin{array}{ccc}
+ 2 & -4 & \frac{1}{4} \\
+ 7 & -\frac{13}{4} & -3 \\
+ -6 & 5 & \frac{19}{4} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/powers_and_exp/4005.txt

@@ -0,0 +1,15 @@
+Problem:
+Compute
+$\left(
+\begin{array}{cc}
+ 2 & \frac{1}{2} \\
+ -\frac{1}{2} & 0 \\
+\end{array}
+\right)^2$.
+Answer:
+$\left(
+\begin{array}{cc}
+ \frac{15}{4} & 1 \\
+ -1 & -\frac{1}{4} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/powers_and_exp/40828.txt

@@ -0,0 +1,15 @@
+Problem:
+Compute
+$\left(
+\begin{array}{cc}
+ 5+\frac{i}{2} & -1-\frac{9 i}{2} \\
+ -\frac{3}{2}-\frac{7 i}{2} & -3+\frac{5 i}{2} \\
+\end{array}
+\right)^2$.
+Answer:
+$\left(
+\begin{array}{cc}
+ \frac{21}{2}+\frac{61 i}{4} & \frac{23}{2}-12 i \\
+ \frac{15}{2}-\frac{23 i}{2} & -\frac{23}{2}-\frac{19 i}{4} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/powers_and_exp/48480.txt

@@ -0,0 +1,19 @@
+Problem:
+Compute
+$e^\left(
+\begin{array}{cccc}
+ 2 & 0 & 0 & 0 \\
+ 4 & -2 & 0 & 0 \\
+ 2 & 0 & 1 & 1 \\
+ 1 & 0 & 0 & 2 \\
+\end{array}
+\right)$.
+Answer:
+$\left(
+\begin{array}{cccc}
+ e^2 & 0 & 0 & 0 \\
+ \frac{e^4-1}{e^2} & \frac{1}{e^2} & 0 & 0 \\
+ 2 e^2-e & 0 & e & e^2-e \\
+ e^2 & 0 & 0 & e^2 \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/powers_and_exp/5332.txt

@@ -0,0 +1,15 @@
+Problem:
+Compute
+$\left(
+\begin{array}{cc}
+ -4+\frac{3 i}{2} & \frac{7}{2}-\frac{7 i}{2} \\
+ 1+4 i & -3+\frac{7 i}{2} \\
+\end{array}
+\right)^2$.
+Answer:
+$\left(
+\begin{array}{cc}
+ \frac{125}{4}-\frac{3 i}{2} & -7+42 i \\
+ -27-23 i & \frac{57}{4}-\frac{21 i}{2} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/powers_and_exp/5748.txt

@@ -0,0 +1,15 @@
+Problem:
+Compute
+$\left(
+\begin{array}{cc}
+ -1 & -4-i \\
+ -\frac{9}{2} & -5 \\
+\end{array}
+\right)^3$.
+Answer:
+$\left(
+\begin{array}{cc}
+ -127-\frac{63 i}{2} & -\frac{383}{2}-67 i \\
+ -\frac{441}{2}-\frac{81 i}{4} & -323-\frac{99 i}{2} \\
+\end{array}
+\right)$

pretraining/mathematica/linear_algebra/powers_and_exp/6985.txt

@@ -0,0 +1,17 @@
+Problem:
+Compute
+$\left(
+\begin{array}{ccc}
+ -3+2 i & 2+2 i & \frac{7}{2}+3 i \\
+ 5-i & \frac{5}{2}-3 i & 5-\frac{i}{2} \\
+ \frac{9}{2}-4 i & -1-\frac{9 i}{2} & -3-5 i \\
+\end{array}
+\right)^3$.
+Answer:
+$\left(
+\begin{array}{ccc}
+ -\frac{349}{2}-\frac{201 i}{2} & -26+\frac{137 i}{8} & \frac{479}{4}+\frac{271 i}{4} \\
+ -\frac{133}{2}-\frac{1727 i}{8} & -\frac{1085}{8}-\frac{531 i}{4} & -48-\frac{1391 i}{8} \\
+ \frac{273}{2}+\frac{53 i}{2} & -\frac{233}{4}-\frac{505 i}{8} & -\frac{1597}{8}-\frac{327 i}{2} \\
+\end{array}
+\right)$

pretraining/mathematica/number_theory/multiplicative_order/10384.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $283^m \equiv 1 \pmod{670}$.
+Answer:
+$44$

pretraining/mathematica/number_theory/multiplicative_order/11677.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $63^m \equiv 1 \pmod{134}$.
+Answer:
+$66$

pretraining/mathematica/number_theory/multiplicative_order/12208.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $92^m \equiv 1 \pmod{531}$.
+Answer:
+$174$

pretraining/mathematica/number_theory/multiplicative_order/12261.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $753^m \equiv 1 \pmod{799}$.
+Answer:
+$16$

pretraining/mathematica/number_theory/multiplicative_order/15638.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $98^m \equiv 1 \pmod{201}$.
+Answer:
+$66$

pretraining/mathematica/number_theory/multiplicative_order/15802.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $113^m \equiv 1 \pmod{216}$.
+Answer:
+$18$

pretraining/mathematica/number_theory/multiplicative_order/17452.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $430^m \equiv 1 \pmod{739}$.
+Answer:
+$738$

pretraining/mathematica/number_theory/multiplicative_order/17529.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $17^m \equiv 1 \pmod{161}$.
+Answer:
+$66$

pretraining/mathematica/number_theory/multiplicative_order/17729.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $611^m \equiv 1 \pmod{917}$.
+Answer:
+$390$

pretraining/mathematica/number_theory/multiplicative_order/18649.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $835^m \equiv 1 \pmod{957}$.
+Answer:
+$14$

pretraining/mathematica/number_theory/multiplicative_order/19846.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $3^m \equiv 1 \pmod{35}$.
+Answer:
+$12$

pretraining/mathematica/number_theory/multiplicative_order/20498.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $736^m \equiv 1 \pmod{769}$.
+Answer:
+$256$

pretraining/mathematica/number_theory/multiplicative_order/20895.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $127^m \equiv 1 \pmod{471}$.
+Answer:
+$78$

pretraining/mathematica/number_theory/multiplicative_order/20960.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $749^m \equiv 1 \pmod{802}$.
+Answer:
+$400$

pretraining/mathematica/number_theory/multiplicative_order/21904.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $23^m \equiv 1 \pmod{42}$.
+Answer:
+$6$

pretraining/mathematica/number_theory/multiplicative_order/22163.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $4^m \equiv 1 \pmod{5}$.
+Answer:
+$2$

pretraining/mathematica/number_theory/multiplicative_order/22207.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $57^m \equiv 1 \pmod{656}$.
+Answer:
+$10$

pretraining/mathematica/number_theory/multiplicative_order/22218.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $167^m \equiv 1 \pmod{266}$.
+Answer:
+$18$

pretraining/mathematica/number_theory/multiplicative_order/22321.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $268^m \equiv 1 \pmod{301}$.
+Answer:
+$21$

pretraining/mathematica/number_theory/multiplicative_order/23167.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $269^m \equiv 1 \pmod{809}$.
+Answer:
+$808$

pretraining/mathematica/number_theory/multiplicative_order/24450.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $217^m \equiv 1 \pmod{732}$.
+Answer:
+$5$

pretraining/mathematica/number_theory/multiplicative_order/24452.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $411^m \equiv 1 \pmod{620}$.
+Answer:
+$10$

pretraining/mathematica/number_theory/multiplicative_order/25906.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $509^m \equiv 1 \pmod{545}$.
+Answer:
+$54$

pretraining/mathematica/number_theory/multiplicative_order/26017.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $480^m \equiv 1 \pmod{491}$.
+Answer:
+$490$

pretraining/mathematica/number_theory/multiplicative_order/26144.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $872^m \equiv 1 \pmod{969}$.
+Answer:
+$144$

pretraining/mathematica/number_theory/multiplicative_order/26421.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $7^m \equiv 1 \pmod{248}$.
+Answer:
+$30$

pretraining/mathematica/number_theory/multiplicative_order/27011.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $786^m \equiv 1 \pmod{857}$.
+Answer:
+$107$

pretraining/mathematica/number_theory/multiplicative_order/28416.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $279^m \equiv 1 \pmod{286}$.
+Answer:
+$60$

pretraining/mathematica/number_theory/multiplicative_order/28619.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $218^m \equiv 1 \pmod{299}$.
+Answer:
+$66$