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  4. The matrix [ λ&-1& 4 [0.3em] -3& 0 1 [0.3em] -1 1 2] is invertible , if

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Q. The matrix $\begin{bmatrix} \lambda&-1& 4 \\[0.3em] -3& 0 & 1\\[0.3em] -1 & 1 & 2\end{bmatrix}$ is invertible , if

Matrices

Solution:

For invertible matrix, $\begin{vmatrix}\lambda&-1&4\\ -3&0&1\\ -1&1&2\end{vmatrix}\ne0$
$\Rightarrow $ $\lambda (0 - 1) + 1 (- 6+ 1) + 4 (-3 - 0) \neq 0$
$\Rightarrow $ $- \lambda - 5 - 12 \neq 0 $
$\Rightarrow \, \lambda \, \neq - 17 \,$