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Matrics — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsMatrics1 Mark
Question
Check whether the following matrices are invertible or not. : $\left[\begin{array}{lll}3 & 4 & 3 \\ 1 & 1 & 0 \\ 1 & 4 & 5\end{array}\right]$
✓

Answer

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

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