Use Inverses to Solve Matrix Equations
Write the Linear System $$\begin{array} { l } 5 x + 2 y - 2 z = 37 \\4 x + 3 y + 5 z = 22 \\7 x - 2 y + 6 z = 15\end{array}$$

question 66

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.
- $$\begin{array} { l } 5 x + 2 y - 2 z = 37 \\4 x + 3 y + 5 z = 22 \\7 x - 2 y + 6 z = 15\end{array}$$

• A)
• \[\left[ \begin{array} { r r r }
• 5 & 2 & - 2 \\
• 4 & 3 & 5 \\
• 7 & - 2 & 6
• \end{array} \right] \left[ \begin{array} { l }
• x \\
• y \\
• z
• \end{array} \right] = \left[ \begin{array} { l }
• 37 \\
• 22 \\
• 15
• \end{array} \right]\]
• B) \(\left[ \begin{array} { c c r } 5 & 4 & 7 \\ 2 & 3 & - 2 \\ - 2 & 5 & 6 \end{array} \right] \left[ \begin{array} { l } x \\ y \\ z \end{array} \right] = \left[ \begin{array} { l } 37 \\ 22 \\ 15 \end{array} \right]\)
• C)
• \[\left[ \begin{array} { r r r }
• 37 & - 2 & 2 \\
• 22 & 5 & 3 \\
• 15 & 6 & - 2
• \end{array} \right] \left[ \begin{array} { l }
• x \\
• y \\
• z
• \end{array} \right] = \left[ \begin{array} { l }
• 5 \\
• 4 \\
• 7
• \end{array} \right]\]
• D)
• \[\left[ \begin{array} { l l }
• 5 & 2 \\
• 4 & 3 \\
• 7 & - 2
• \end{array} \right] \left[ \begin{array} { l }
• x \\
• y \\
• z
• \end{array} \right] = \left[ \begin{array} { l }
• - 2 \\
• 5 \\
• 6
• \end{array} \right]\]

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