If $A=\begin{bmatrix} 2 & 3\\-1 & 1\end{bmatrix} $ and $A^2-3A+kI=0$ then the value of k is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 5
$A=\begin{bmatrix} 2 & 3\\-1 & 1\end{bmatrix}$
$A^2=\begin{bmatrix} 2 & 3\\-1 & 1\end{bmatrix}\begin{bmatrix} 2 & 3\\-1 & 1\end{bmatrix}=\begin{bmatrix} 1 & 9\\-3 & -2\end{bmatrix}$
$kI=3A-A^2$
$=\begin{bmatrix} 6 & 9\\-3 & 3\end{bmatrix}-\begin{bmatrix} 1 & 9\\-3 & -2\end{bmatrix}=\begin{bmatrix} 5 & 0\\0 & 5\end{bmatrix}$
$k=5$