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

Q6. $\begin{bmatrix} 2 & 5\\ 1 &3 \end{bmatrix}$

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

$A=IA$

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

Use the elementary transformation

$R_1\rightarrow R_1-R_2$

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

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

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

$R_1\rightarrow R_1-2R_2$

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

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

Posted by

seema garhwal

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