Let matrix $A=\left[\begin{array}{ccc}5 & -3 & 0 \\ -3 & 5 & 0 \\ 0 & 0 & 2\end{array}\right], X$ be a non…
Let matrix $A=\left[\begin{array}{ccc}5 & -3 & 0 \\ -3 & 5 & 0 \\ 0 & 0 & 2\end{array}\right], X$ be a non zero matrix of order $3 \times 1$ and $c$ be a real number. If $A^2 X=c A X$, then the number of distinct values of $c$ is
3
2
1
0
Solution
Given,
$
\begin{aligned}
A^2 x & =c A x \rightarrow A \\
A x & =\mathcal{c}
\end{aligned}
$
$A x \rightarrow c$ is eigen value of $A$.
$\therefore$ Eigen value of $A$ are $8,2,2$
Therefore, number of values of $c$ is 2