Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine Problem 186
Show that \(E^{2} F+F^{2} E=E\), where \(E=\left[\begin{array}{lll}0 & 0 & 1 \\\ 0 & 0 & 1 \\ 0 & 0 & 0\end{array}\right], F=\left[\begin{array}{lll}1 & 0 & 0 \\\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]\).
Problem 187
Find \(x\) so that \(\left[\begin{array}{lll}1 & x & 1\end{array}\right]\left[\begin{array}{lll}1 & 3 & 2 \\ 0 & 5 & 1 \\ 0 & 3 & 2\end{array}\right]\left[\begin{array}{l}1 \\ 1 \\ x\end{array}\right]=O\).
Problem 188
If \(A=\left[\begin{array}{cc}0.8 & 0.6 \\ -0.6 & 0.8\end{array}\right]\), find \(A^{3} .\)
Problem 189
If \(X=\left[\begin{array}{cc}3 & -4 \\ 1 & -1\end{array}\right]\), then find \(X^{3}\).
Problem 190
If \(A=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]\), then find \(A^{11}\).
Problem 191
If \(J_{1}=\left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right]\) and \(J_{2}=\left[\begin{array}{cc}1 & 0 \\ -1 & 0\end{array}\right]\), then find \(J_{1}^{2}+J_{2}^{2}\).
Problem 192
If \(A=\left[\begin{array}{ccc}1 & -3 & 2 \\ 2 & 1 & -3 \\ 4 & -3 & -1\end{array}\right], B=\left[\begin{array}{cc}1 & 4 \\ 2 & 1 \\ 1 & -2\end{array}\right]\) and \(C=\left[\begin{array}{ccc}2 & 1 & -1 \\ 3 & -2 & -1\end{array}\right]\). Show that \((A B) C=A(B C)\).
Problem 193
If \(f(x)=x^{2}-5 x+6 I\), find \(f(A)\) if \(A=\left[\begin{array}{ccc}2 & 0 & 1 \\\ 2 & 1 & 3 \\ 1 & -1 & 0\end{array}\right]\).
Problem 194
If \(A=\left[\begin{array}{ll}2 & 4 \\ 4 & 3\end{array}\right], X=\left[\begin{array}{l}n \\ 1\end{array}\right], B=\left[\begin{array}{c}8 \\\ 11\end{array}\right]\) and \(A X=B\), then find \(n\).
Problem 195
If \(A=\left[\begin{array}{ll}a & b \\ b & a\end{array}\right]\) and \(A^{2}=\left[\begin{array}{ll}\alpha & \beta \\ \beta & \alpha\end{array}\right]\), then show that \(\alpha=a^{2}+b^{2}, \beta=2 a b\).
