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Using elementary transformations, find the inverse of each of the matrices, if it exists
in Exercises 1 to 17.

Q13. $\begin{bmatrix} 2 & -3\\ -1 & 2 \end{bmatrix}$

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$A=\begin{bmatrix} 2 & -3\\ -1 & 2 \end{bmatrix}$

$A=IA$

$\Rightarrow$ $\begin{bmatrix} 2 & -3\\ -1 & 2 \end{bmatrix}$ $= \begin{bmatrix}1&0\\0&1 \end{bmatrix}A$

$R_2\rightarrow 2R_2+R_1$

$\Rightarrow$ $\begin{bmatrix} 2 & -3\\ 0 &1 \end{bmatrix}$ $= \begin{bmatrix}1&0\\1&2 \end{bmatrix}A$

$\Rightarrow$ $R_1\rightarrow R_1+3R_2$

$\Rightarrow$ $\begin{bmatrix} 2 & 0\\ 0 &1 \end{bmatrix}$ $= \begin{bmatrix}4&6\\1&2 \end{bmatrix}A$

$R_1\rightarrow \frac{R_1}{2}$

$\Rightarrow$ $\begin{bmatrix} 1 & 0\\ 0 &1 \end{bmatrix}$ $= \begin{bmatrix}2&3\\1&2 \end{bmatrix}A$

so the inverse of matrix A is

$\therefore A^{-1}=$ $\begin{bmatrix}2&3\\1&2 \end{bmatrix}$ .

Posted by

seema garhwal

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