Check whether following matrices are invertible or not: [ lll 3 &… - Vidyadip

Question

Check whether following matrices are invertible or not: $\left[\begin{array}{lll}3 & 4 & 3 \\ 1 & 1 & 0 \\ 1 & 4 & 5\end{array}\right]$

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Answer

Let $A=\left[\begin{array}{lll}3 & 4 & 3 \\ 1 & 1 & 0 \\ 1 & 4 & 5\end{array}\right]$
Then $|A|=\left|\begin{array}{lll}3 & 4 & 3 \\ 1 & 1 & 0 \\ 1 & 4 & 5\end{array}\right|$
$
\begin{aligned}
& =3(5-0)-4(5-0)+3(4-1) \\
& =15-20+9 \\
& =4 \neq 0
\end{aligned}
$
$\therefore A$ is a non-singular matrix.
Hence, $A ^{-1}$ exists.

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