Mccoy Sullivan

08/01/2023 · Junior High School

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