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  • Using elementary transformations, find the inverse of each of the matrices, if it exists in Exercises 1 to 17. [ 1 3 2 7]

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

    Q3.    \begin{bmatrix} 1 &3 \\ 2 & 7 \end{bmatrix}

Answers (1)

best_answer

A=\begin{bmatrix} 1 &3 \\ 2 & 7 \end{bmatrix}

                A=IA

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

Using elementary transformations

             R_2\rightarrow R_2-2R_1

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

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

 

 

Posted by

seema garhwal

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