Find k _ , if [ ll 7 & 3 5 & k ] is a singular matrix. - Vidyadip

Question

Find $k _{\text {, if }}\left[\begin{array}{ll}7 & 3 \\ 5 & k\end{array}\right]$ is a singular matrix.

✓

Answer

Let $A=\left[\begin{array}{ll}7 & 3 \\ 5 & k\end{array}\right]$
Since, $A$ is singular matrix, $|A|=0$
$
\begin{aligned}
& \therefore\left|\begin{array}{cc}
7 & 3 \\
5 & k
\end{array}\right|=0 \\
& \therefore 7 k -15=0 \\
& \therefore k =\frac{15}{7}
\end{aligned}
$

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