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

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Matrices (p-1)2 Marks
Question
Which of the following matrices are singular or non-singular : $\left[\begin{array}{ccc}a & b & c \\ p & q & r \\ 2 a-p & 2 b-q & 2 c-r\end{array}\right]$
✓

Answer

Let $A =\left[\begin{array}{ccc}a & b & c \\ p & q & r \\ 2 a-p & 2 b-q & 2 c-r\end{array}\right]$
$
\therefore| A |=\left|\begin{array}{ccc}
a & b & c \\
p & q & r \\
2 a-p & 2 b-q & 2 c-r
\end{array}\right|
$
By $R_3+R_2$, we get,
$
\begin{aligned}
| A | & =\left|\begin{array}{ccc}
a & b & c \\
p & q & r \\
2 a & 2 b & 2 c
\end{array}\right| \\
& =2\left|\begin{array}{lll}
a & b & c \\
p & q & r \\
a & b & c
\end{array}\right| \\
& =2 \times 0 \\
& =0
\end{aligned}
$
$\therefore A$ is a singular matrix.

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