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

Q4. $\begin{bmatrix} 2 &3 \\ 5 & 7 \end{bmatrix}$

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$A=\begin{bmatrix} 2 &3 \\ 5 & 7 \end{bmatrix}$

$A=IA$

$\Rightarrow$ $\begin{bmatrix} 2 &3 \\ 5 & 7 \end{bmatrix}$ $= \begin{bmatrix}1&0\\0&1 \end{bmatrix}A$

$R_2\rightarrow R_2-2R_1$

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

$\Rightarrow$ $R_1\rightarrow R_1-3R_2$

$\Rightarrow$ $\begin{bmatrix} -1 &0 \\ 1 & 1 \end{bmatrix}$ $= \begin{bmatrix}7&-3\\-2&1 \end{bmatrix}A$

$R_2\rightarrow R_2+R_1$

$\Rightarrow$ $\begin{bmatrix} -1 &0 \\ 0 & 1 \end{bmatrix}$ $= \begin{bmatrix}7&-3\\5&-2\end{bmatrix}A$

$R_1\rightarrow -R_1$

$\Rightarrow$ $\begin{bmatrix} 1 &0 \\ 0 & 1 \end{bmatrix}$ $= \begin{bmatrix}-7&3\\5&-2\end{bmatrix}A$

$\therefore A^{-1}=$ $\begin{bmatrix}-7&3\\5&-2\end{bmatrix}$

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seema garhwal

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