(B)
\[
\left\{\begin{array}{l}
2 x-3 y-z=0 \\
-2 x+y+2 z=-9 \\
4 x+2 y+z=1
\end{array}\right.
\]

Answer

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Answer

\(\boxed{x = 0.5, y = 2, z = -5}\)

Steps

Step 1 ：\(\left\{\begin{array}{l} 2x-3y-z=0 \\ -2x+y+2z=-9 \\ 4x+2y+z=1 \end{array}\right.\)

Step 2 ：Use matrix operations to solve the system of linear equations.

Step 3 ：\(\begin{bmatrix} 2 & -3 & -1 \\ -2 & 1 & 2 \\ 4 & 2 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 0 \\ -9 \\ 1 \end{bmatrix}\)

Step 4 ：\(\begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 0.5 \\ 2 \\ -5 \end{bmatrix}\)

Step 5 ：\(\boxed{x = 0.5, y = 2, z = -5}\)

(B)\[\left\{\begin{array}{l}2 x-3 y-z=0 \\-2 x+y+2 z=-9 \\4 x+2 y+z=1\end{array}\right.\]

Answer

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(B)
\[
\left\{\begin{array}{l}
2 x-3 y-z=0 \\
-2 x+y+2 z=-9 \\
4 x+2 y+z=1
\end{array}\right.
\]