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

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

Wang Parry · 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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