Find k, if the following matrices are singular: [ cc 7 & 3 -2 & K… - Vidyadip

Question

Find k, if the following matrices are singular:$\left[\begin{array}{cc}7 & 3 \\ -2 & K\end{array}\right]$

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Answer

Let $A =\left[\begin{array}{cc}7 & 3 \\ -2 & K\end{array}\right]$
Since, $A$ is a singular matrix, $|A|=0$
$
\begin{aligned}
& \therefore\left|\begin{array}{cr}
7 & 3 \\
-2 & k
\end{array}\right|=0 \\
& \therefore 7 k -(-6)=0 \\
& \therefore 7 k =-6 \\
& \therefore k =-\frac{6}{7}
\end{aligned}
$

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