Blake Osborne
02/01/2023 · Middle School
\( \begin{array}{l}x+y-z=2 \\ 3 x+2 y-z=-3 \\ -x-y+2 z=-1 \\ \text { Write down the system in matrix form, }\end{array} \) \( A X=b \) 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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Quick Answer
The coefficient matrix \( A \) is:
\[
A = \begin{bmatrix}
1 & 1 & -1 \\
3 & 2 & -1 \\
-1 & -1 & 2
\end{bmatrix}
\]
The variable matrix \( X \) is:
\[
X = \begin{bmatrix}
x \\
y \\
z
\end{bmatrix}
\]
The constant matrix \( b \) is:
\[
b = \begin{bmatrix}
2 \\
-3 \\
-1
\end{bmatrix}
\]
Matrices \( A \) and \( b \) are both \( 3 \times 1 \) in size.
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