4. For what values of x: \(A=\begin{bmatrix}1&2&1\end{bmatrix}\) \(\begin{bmatrix}1&2&0 \\2&0&1\\1&0&2 \end{bmatrix}\)\(\begin{bmatrix}0\\2\\x \end{bmatrix}=O?\)
Class 12
Matrices
Miscellaneous Exercise
1. If A and B are symmetric matrices, prove that AB–BA is a skew symmetric matrix.
5. If \(A=\begin{bmatrix}3&1 \\ -1&2\end{bmatrix}\), show that \(A^2-5A+7I=0\).
9. If \(A=\begin{bmatrix}α&β \\ γ &-α\end{bmatrix}\) is such that \(A^2=I\), then
(A) \(1+α^2+βγ=0\)
(B) \(1-α^2+βγ=0\)
(C) \(1-α^2-βγ=0\)
(D) \(1+α^2-βγ=0\).
10. If the matrix A is both symmetric and skew symmetric, then
(A) A is a diagonal matrix
(B) A is a zero matrix
(C) A is a square matrix
(D) None of these
11. If A is square matrix such that \(A^2=A\), then \((I+A)^3–7A\) is equal to
(A) A
(B) I–A
(C) I
(D) 3A