Given $X=\begin{bmatrix}1 & 0\\-1 & 7 \end{bmatrix},$ then value of K if $X^2=8X+KI $ is :
Answer & explanation
Correct answer: option 1
$X=\begin{bmatrix}1&0\\-1&7\end{bmatrix}.$
$X^2=\begin{bmatrix}1&0\\-8&49\end{bmatrix}.$
$-8X=\begin{bmatrix}-8&0\\8&-56\end{bmatrix}.$
$X^2-8X=\begin{bmatrix}-7&0\\0&-7\end{bmatrix}.$
$X^2-8X+KI=\begin{bmatrix}-7+K&0\\0&-7+K\end{bmatrix}.$
$\text{For zero matrix, }-7+K=0.$
$K=7.$