# Using elementary transformations, find the inverse of each of the matrices, if it exists in Exercises 1 to 17.    Q14.    $\begin{bmatrix} 2 & 1\\ 4 & 2 \end{bmatrix}$

S seema garhwal

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

$A=IA$

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

$R_2\rightarrow \frac{R_2}{2}$

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

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

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

Hence, we can see all upper values of matirix are zeros in L.H.S  so $A^{-1}$ does not exists.

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