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

question 88

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.

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