Check whether following matrices are invertible or not: [ lll 1 &… - Vidyadip

Question

Check whether following matrices are invertible or not: $\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 4 & 5 \\ 2 & 4 & 6\end{array}\right]$

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Answer

Let $A=\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 4 & 5 \\ 2 & 4 & 6\end{array}\right]$
Then $|A|=\left|\begin{array}{lll}1 & 2 & 3 \\ 2 & 4 & 5 \\ 2 & 4 & 6\end{array}\right|$
$
\begin{aligned}
& =1(24-20)-2(12-10)+3(8-8) \\
& =4-4+0 \\
& =0
\end{aligned}
$
$\therefore A$ is a singular matrix.
Hence, A-1 does not exist.

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