GATE (TF) Textile 2021 Question Paper Solution | GATE/2021/TF/42

If 3 and 6 are eigen value of the matrix
$\begin{bmatrix} 5 & 2 & 0\\ 2 & \mu & 0\\ -3 & 4 & 6 \end{bmatrix}$
then value of $\mu$ is __5___.

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Let, A= $\begin{bmatrix} 5 & 2 & 0\\ 2 & \mu & 0\\ -3 & 4 & 6 \end{bmatrix}$

AI=B

$A-\lambda I=0$

A= $\begin{bmatrix} 5-\lambda & 2 & 0\\ 2 & \mu-\lambda & 0\\ -3 & 4 & 6-\lambda \end{bmatrix}$

Solve the matrix

$\mu=5$ (Ans)