Which of the following matrices are singular or non-singular : [ … - Vidyadip

Question

Which of the following matrices are singular or non-singular : $\left[\begin{array}{cc}7 & 5 \\ -4 & 7\end{array}\right]$

✓

Answer

$
\begin{aligned}
& \text { Let } D=\left[\begin{array}{cc}
7 & 5 \\
-4 & 7
\end{array}\right] \\
& \therefore|D|=\left|\begin{array}{cc}
7 & 5 \\
-4 & 7
\end{array}\right| \\
& =49-(-20) \\
& =69 \neq 0
\end{aligned}
$
$\therefore D$ is a non-singular matrix.

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