Consider the system of linear equations $$ \begin{array}{l}x+y-z=2 \ 3 x+2 y-z=3 \ -x-y+2 z=-1 \ ext { Write down the system in matrix form, } \ A X=b ext { where } X=\left[\begin{array}{c}x \ y \ z\end{array} ight] \ ext { Write down the coefficient matrix } A ext { of the above system. Determine } \ ext { the inverse } A ext { of } A ext { by applying the matrix inverse algorithm, that } \ ext { is by applying the sequence of elementary row operations in the } \ ext { sense }\left[A \mid I_{3} ight] \ ext { where } I_{3} ext { is the } 3 ext { by } 3 ext { identity matrix. }\end{array} $$.

Question

Consider the system of linear equations $$ \begin{array}{l}x+y-z=2 \ 3 x+2 y-z=3 \ -x-y+2 z=-1 \ 	ext { Write down the system in matrix form, } \ A X=b 	ext { where } X=\left[\begin{array}{c}x \ y \ z\end{array}ight] \ 	ext { Write down the coefficient matrix } A 	ext { of the above system. Determine } \ 	ext { the inverse } A 	ext { of } A 	ext { by applying the matrix inverse algorithm, that } \ 	ext { is by applying the sequence of elementary row operations in the } \ 	ext { sense }\left[A \mid I_{3}ight] \ 	ext { where } I_{3} 	ext { is the } 3 	ext { by } 3 	ext { identity matrix. }\end{array} $$.

Pena Lyons · Accepted Answer

The coefficient matrix $$A$$ is: $$ A = \begin{bmatrix} 1 & 1 & -1 \ 3 & 2 & -1 \ -1 & -1 & 2 \end{bmatrix} $$ The inverse of matrix $$A$$ is: $$ A^{-1} = \begin{bmatrix} -3 & 1 & -1 \ 5 & -1 & 2 \ 1 & 0 & 1 \end{bmatrix} $$

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