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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. : $\left[\begin{array}{lll}1 & 2 & 3 \\ 3 & 4 & 5 \\ 4 & 6 & 8\end{array}\right]$
✓

Answer

Let $A=\left[\begin{array}{lll}1 & 2 & 3 \\ 3 & 4 & 5 \\ 4 & 6 & 8\end{array}\right]$
Then, $|\mathrm{A}|=\left|\begin{array}{lll}1 & 2 & 3 \\ 3 & 4 & 5 \\ 4 & 6 & 8\end{array}\right|$
$= 1(32 – 30) – 2(24 – 20) + 3(18 – 16)$
$= 2 – 8 + 6 = 0$
$\therefore $ A is a singular matrix.
Hence,$A^{-1}$ does not exist.

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