Problem

$\left\{\begin{array}{l}x-2 y-2 z=-1 \\ x-y+z=-2 \\ 2 x+y+3 z=1\end{array}\right.$

Answer

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Answer

\(\boxed{x = 1, y = 2, z = -1}\)

Steps

Step 1 :\(\left\{\begin{array}{l}x-2 y-2 z=-1 \\ x-y+z=-2 \\ 2 x+y+3 z=1\end{array}\right.\)

Step 2 :\(A = \begin{bmatrix} 1 & -2 & -2 \\ 1 & -1 & 1 \\ 2 & 1 & 3 \end{bmatrix}, B = \begin{bmatrix} -1 \\ -2 \\ 1 \end{bmatrix}\)

Step 3 :\(\text{solution} = \begin{bmatrix} 1 \\ 2 \\ -1 \end{bmatrix}\)

Step 4 :\(\boxed{x = 1, y = 2, z = -1}\)

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