Tyler Fitzgerald
04/01/2024 · Senior High School

Consider the system of linear equations \( \begin{array}{l}x+y-z=2 \\ 3 x+2 y-z=-3 \\ -x-y+2 z=-1\end{array} \) Write down the system in matrix form, \( A X=b \) where \( X=\left[\begin{array}{l}x \\ y \\ z\end{array}\right] \) Write down the matrices \( A \) and \( b \) as well as their respective sizes:

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Matrix \( A \) is \( \begin{bmatrix} 1 & 1 & -1 \\ 3 & 2 & -1 \\ -1 & -1 & 2 \end{bmatrix} \), a 3x3 matrix, and vector \( b \) is \( \begin{bmatrix} 2 \\ -3 \\ -1 \end{bmatrix} \), a 3x1 vector.

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