Use Inverses to Solve Matrix Equations
-$$\begin{array} { l }
5 x + 2 y + 2 z = 32 \
4 x + 2 y - 2 z = 32 \
8 x + 2 y + 8 z = 38
\end{array}$$
A)
$\left[ \begin{array} { r r r } 5 & 2 & 2 \ 4 & 2 & - 2 \ 8 & 2 & 8 \end{array} \right] \left[ \begin{array} { l } x \ y \ z \end{array} \right] = \left[ \begin{array} { l } 32 \ 32 \ 38 \end{array} \right]$
B)
$\left[ \begin{array} { r r r } 5 & 4 & 8 \ 2 & 2 & 2 \ 2 & - 2 & 8 \end{array} \right] \left[ \begin{array} { l } \mathrm { x } \ \mathrm { y } \ \mathrm { z } \end{array} \right] = \left[ \begin{array} { l } 32 \ 32 \ 38 \end{array} \right]$
C)
$$\left[ \begin{array} { r r r }
32 & 2 & 2 \
32 & - 2 & 2 \
38 & 8 & 2
\end{array} \right] \left[ \begin{array} { l }
x \
y \
z
\end{array} \right] = \left[ \begin{array} { l }
5 \
4 \
8
\end{array} \right]$$
D)
$$\left[ \begin{array} { l l }
5 & 2 \
4 & 2 \
8 & 2
\end{array} \right] \left[ \begin{array} { l }
x \
y \
z
\end{array} \right] = \left[ \begin{array} { l }
2 \
- 2 \
8
\end{array} \right]$$

Question

Use Inverses to Solve Matrix Equations
-$$\begin{array} { l } 
5 x + 2 y + 2 z = 32 \
4 x + 2 y - 2 z = 32 \
8 x + 2 y + 8 z = 38
\end{array}$$
A)
$\left[ \begin{array} { r r r } 5 & 2 & 2 \ 4 & 2 & - 2 \ 8 & 2 & 8 \end{array} \right] \left[ \begin{array} { l } x \ y \ z \end{array} \right] = \left[ \begin{array} { l } 32 \ 32 \ 38 \end{array} \right]$
B)
$\left[ \begin{array} { r r r } 5 & 4 & 8 \ 2 & 2 & 2 \ 2 & - 2 & 8 \end{array} \right] \left[ \begin{array} { l } \mathrm { x } \ \mathrm { y } \ \mathrm { z } \end{array} \right] = \left[ \begin{array} { l } 32 \ 32 \ 38 \end{array} \right]$
C)
$$\left[ \begin{array} { r r r } 
32 & 2 & 2 \
32 & - 2 & 2 \
38 & 8 & 2
\end{array} \right] \left[ \begin{array} { l } 
x \
y \
z
\end{array} \right] = \left[ \begin{array} { l } 
5 \
4 \
8
\end{array} \right]$$
D)
$$\left[ \begin{array} { l l } 
5 & 2 \
4 & 2 \
8 & 2
\end{array} \right] \left[ \begin{array} { l } 
x \
y \
z
\end{array} \right] = \left[ \begin{array} { l } 
2 \
- 2 \
8
\end{array} \right]$$

Quizplus · Accepted Answer

The correct matrix equation is formed by arranging the coefficients of $x$, $y$, and $z$ from the given system of equations into a matrix, aligning with the variables $x$, $y$, and $z$ in a column matrix, and setting this equal to the column matrix of the constants on the right-hand side of the equations. Option A correctly represents this setup.

Use Inverses to Solve Matrix Equations - 5x+2y+2z=324x+2y−2z=328x+2y+8z=38\begin{array} { l } 5 x + 2 y + 2 z = 32 \\4 x + 2 y - 2 z = 32 \\8 x + 2 y + 8 z = 38\end{array}5x+2y+2z=324x+2y−2z=328x+2y+8z=38​

Use Inverses to Solve Matrix Equations
- $\begin{array} { l } 5 x + 2 y + 2 z = 32 \\4 x + 2 y - 2 z = 32 \\8 x + 2 y + 8 z = 38\end{array}$