The matrix $A=\left[\begin{array}{ccc}a & -1 & 4 \ -3 & 0 & 1 \ -1 & 1 & 2\end{array} ight]$ is not invertible only if a =

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The matrix $A=\left[\begin{array}{ccc}a & -1 & 4 \ -3 & 0 & 1 \ -1 & 1 & 2\end{array}ight]$ is not invertible only if a =

Aicharya · Accepted Answer

Since $\mathrm{A}$ is not invertible, $|\mathrm{A}|=0$ $\begin{aligned} 	herefore &\left|\begin{array}{ccc}a & -1 & 4 \ -3 & 0 & 1 \ -1 & 1 & 2\end{array}ight|=0 \ & \mathrm{a}(0-1)-(-1)(-6+1)+4(-3-0)=0 \Rightarrow-\mathrm{a}-5-12=0 \Rightarrow \mathrm{a}=-17 \end{aligned}$

The matrix $A=\left[\begin{array}{ccc}a & -1 & 4 \\ -3 & 0 & 1 \\ -1 & 1 & 2\end{array}\right]$ is not…

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