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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 : $\left[\begin{array}{ccc}5 & 0 & 5 \\ 1 & 99 & 100 \\ 6 & 99 & 105\end{array}\right]$
✓

Answer

Let $B=\left(\begin{array}{rrr}5 & 0 & 5 \\ 1 & 99 & 100 \\ 6 & 99 & 105\end{array}\right)$
$
\therefore| B |=\left|\begin{array}{rrr}
5 & 0 & 5 \\
1 & 99 & 100 \\
6 & 99 & 105
\end{array}\right|
$
By $R_3-R_2$, we get
$
\begin{aligned}
|B| & =\left|\begin{array}{rrr}
5 & 0 & 5 \\
1 & 99 & 100 \\
5 & 0 & 5
\end{array}\right| \\
& =0 \left[\because R_1 \equiv R_3\right]
\end{aligned}
$
$\therefore B$ is a singular matrix.

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