Use Inverses to Solve Matrix Equations
Write the Linear System $$\begin{array} { r } 2 x + 3 z = 17 \\2 y + 7 z = 21 \\2 x + 5 y + 5 z = 54\end{array}$$

Multiple Choice

Use Inverses to Solve Matrix Equations
Write the linear system as a matrix equation in the form AX = B, where A is the coefficient matrix and B is the
constant matrix.
- $$\begin{array} { r } 2 x + 3 z = 17 \\2 y + 7 z = 21 \\2 x + 5 y + 5 z = 54\end{array}$$

A)
$\left[ \begin{array} { l l l } 2 & 0 & 3 \\ 0 & 2 & 7 \\ 2 & 5 & 5 \end{array} \right] \left[ \begin{array} { l } x \\ y \\ z \end{array} \right] = \left[ \begin{array} { l } 17 \\ 21 \\ 54 \end{array} \right]$
B)
$$\left[ \begin{array} { l l l } 2 & 3 & 0 \\2 & 7 & 0 \\2 & 5 & 5\end{array} \right] \left[ \begin{array} { l } x \\y \\z\end{array} \right] = \left[ \begin{array} { c } 17 \\21 \\54\end{array} \right]$$
C)
$$\left[ \begin{array} { l l l } 2 & 0 & 2 \\0 & 2 & 5 \\3 & 7 & 5\end{array} \right] \left[ \begin{array} { l } x \\y \\z\end{array} \right] = \left[ \begin{array} { l } 17 \\21 \\54\end{array} \right]$$
D)
$\left[\begin{array}{ll}2 & 0 \\0 & 2 \\2 & 5\end{array}\right]\left[\begin{array}{l}x \\y \\z\end{array}\right]=\left[\begin{array}{c}3 \\7 \\5\end{array}\right]$

Write the matrix equation as a system of linear equations without matrices.