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Using elementary transformations, find the inverse of each of the matrices, if it exists in Exercises 1 to 17. [2 1 1 1]

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

    Q2.    \begin{bmatrix} 2&1\\1&1\end{bmatrix}

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

                A=IA

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

             R_1\rightarrow R_1-R_2

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

                  R_2\rightarrow R_2-R_1

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

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

Thus we have obtained the inverse of the given matrix through elementary transformation 

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