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  4. If the inverse of the matrix [α&14&-1 2&3&1 6&2&3] does not exist then the value of α is

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Q. If the inverse of the matrix $\begin{bmatrix}\alpha&14&-1\\ 2&3&1\\ 6&2&3\end{bmatrix} $ does not exist then the value of $\alpha$ is

MHT CETMHT CET 2017Determinants

Solution:

$A=\begin{bmatrix}\alpha & 14 & -1 \\ 2 & 3 & 1 \\ 6 & 2 & 3\end{bmatrix}$
$| A |=\alpha[9-2]-14[6-6]-1[4-18]$
$| A |=7 \alpha+14$
$A ^{-1}$ does not exists if $| A |=0$
$\Rightarrow 7 \alpha+14=0 $
$\Rightarrow \alpha=-2$