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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. : $\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & -1 & 3 \\ 1 & 2 & 3\end{array}\right]$
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Answer

Let $A=\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & -1 & 3 \\ 1 & 2 & 3\end{array}\right]$
Then, $|\mathrm{A}|=\left|\begin{array}{lll}1 & 2 & 3 \\ 2 & -1 & 3 \\ 1 & 2 & 3\end{array}\right|$
$= 1 (-3 -6) – 2 (6 – 3) + 3 (4 + 1)$
$= -9 – 6 + 15 = 0$
$\therefore $ A is a singular matrix.
Hence, $A^{-1}$​​​​​​​ does not exist.

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