MCQ
જો $A=\begin{bmatrix}2 & 3 \\ 5 & -2\end{bmatrix}$ હોય, તો $A^{-1}=..........$
- A$ \frac {1}{11} A$
- B$ -\frac {1}{11} A$
- C$ - \frac {1}{19} A$
- ✓$ \frac {1}{19} A$
$|A|=\begin{vmatrix}2 & 3 \\ 5 & -2\end{vmatrix}=-4-15=-19\ne 0$
$ \therefore A^{-1}$ નું અસ્તિત્વ છે.
$adj A = \begin{bmatrix}-2 & -3 \\ -5 & 2\end{bmatrix} $
$A^{-1}=\frac {1}{|A|} adj A$
$= -\frac {1}{19}\begin{bmatrix}-2 & -3 \\ -5 & 2\end{bmatrix}= \frac {1}{19}\begin{bmatrix}2 & 3 \\ 5 & -2\end{bmatrix}$
$ = \frac {1}{19} A$
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