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Matrices (p-1) — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Matrices (p-1)1 Mark
Question
Which of the following matrices are singular or non-singular : $\left[\begin{array}{ccc}3 & 5 & 7 \\ -2 & 1 & 4 \\ 3 & 2 & 5\end{array}\right]$
✓

Answer

$
\begin{aligned}
& \text { Let } C=\left[\begin{array}{ccc}
3 & 5 & 7 \\
-2 & 1 & 4 \\
3 & 2 & 5
\end{array}\right] \\
& \therefore|C|=\left|\begin{array}{rrr}
3 & 5 & 7 \\
-2 & 1 & 4 \\
3 & 2 & 5
\end{array}\right| \\
& =3(5-8)-5(-10-12)+7(-4-3) \\
& =-9+110-49 \\
& =52 \neq 0
\end{aligned}
$
$\therefore C$ is a non-singular matrix.

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