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  4. The matrix [λ -1 4 -3 0 1 -1 1 2] is invertible, if

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Q. The matrix $\begin{bmatrix}\lambda & -1 & 4 \\ -3 & 0 & 1 \\ -1 & 1 & 2\end{bmatrix}$ is invertible, if

Determinants

Solution:

For invertible matrix, $\begin{vmatrix}\lambda & -1 & 4 \\ -3 & 0 & 1 \\ -1 & 1 & 2\end{vmatrix} \neq 0$
$\Rightarrow \lambda(0-1)+1(-6+1)+4(-3-0) \neq 0$
$\Rightarrow \quad-\lambda-5-12 \neq 0$
$ \Rightarrow \lambda \neq-17$