Write the matrix equation as a system of linear equations without matrices.
-$$\left[ \begin{array} { l l l }
3 & 2 & 8 \
9 & 0 & 7 \
4 & 9 & 0
\end{array} \right] \left[ \begin{array} { l }
x \
y \
z
\end{array} \right] = \left[ \begin{array} { r }
- 2 \
4 \
2
\end{array} \right]$$
A) $3 x + 2 y + 8 z = - 2$
$9 x + 7 z = 4$
$4 x + 9 y = 2$
B) $3 x - 2 y + 8 z = - 2$
$9 x + 7 z = - 4$
$4 x + 9 y = - 2$
C) $3 x + 2 y + 8 z = - 2$
$9 x + 7 z = 4$
$4 x + 9 z = 2$
D) $3 x + 2 y + 8 z = - 2$
$9 x + 7 y = 4$
$4 x + 9 z = 2$

Question

Write the matrix equation as a system of linear equations without matrices.
-$$\left[ \begin{array} { l l l } 
3 & 2 & 8 \
9 & 0 & 7 \
4 & 9 & 0
\end{array} \right] \left[ \begin{array} { l } 
x \
y \
z
\end{array} \right] = \left[ \begin{array} { r } 
- 2 \
4 \
2
\end{array} \right]$$
A) $3 x + 2 y + 8 z = - 2$
$9 x + 7 z = 4$
$4 x + 9 y = 2$
B) $3 x - 2 y + 8 z = - 2$
$9 x + 7 z = - 4$
$4 x + 9 y = - 2$
C) $3 x + 2 y + 8 z = - 2$
$9 x + 7 z = 4$
$4 x + 9 z = 2$
D) $3 x + 2 y + 8 z = - 2$
$9 x + 7 y = 4$
$4 x + 9 z = 2$

Quizplus · Accepted Answer

The matrix equation translates directly to the system of linear equations by multiplying the matrix by the vector of variables (x, y, z) to get the resulting vector on the right side. Each row of the matrix corresponds to one equation in the system, with the coefficients of x, y, and z in each equation corresponding to the elements of the matrix in that row.

Write the Matrix Equation as a System of Linear Equations