Solve the System of Linear Equations Using the Inverse Matrix

question 109

Multiple Choice

Solve the system of linear equations
$\left\{ \begin{array} { l } 8 x _ { 1 } - 16 x _ { 2 } - 8 x _ { 3 } - 16 x _ { 4 } = 0 \\24 x _ { 1 } - 40 x _ { 2 } - 16 x _ { 3 } - 24 x _ { 4 } = - 9 \\16 x _ { 1 } - 40 x _ { 2 } - 16 x _ { 3 } - 40 x _ { 4 } = 6 \\- 8 x _ { 1 } + 32 x _ { 2 } + 32 x _ { 3 } + 88 x _ { 4 } = 0\end{array} \right.$
using the inverse matrix $\frac { 1 } { 8 } \left[ \begin{array} { c c c c } - 24 & 7 & 1 & - 2 \\ - 10 & 3 & 0 & - 1 \\ - 29 & 7 & 3 & - 2 \\ 12 & - 3 & - 1 & 1 \end{array} \right]$ .

• A) \(\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \\ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } - \frac { 57 } { 8 } \\ - \frac { 27 } { 8 } \\ - \frac { 45 } { 8 } \\ \frac { 21 } { 8 } \end{array} \right]\)
• B) \(\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \\ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } - \frac { 21 } { 8 } \\ - \frac { 15 } { 8 } \\ \frac { 27 } { 8 } \\ - \frac { 27 } { 8 } \end{array} \right]\)
• C) \(\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \\ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } - \frac { 27 } { 8 } \\ - \frac { 57 } { 8 } \\ 0 \\ \frac { 21 } { 8 } \end{array} \right]\)
• D) \(\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \\ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } - \frac { 9 } { 8 } \\ \frac { 3 } { 8 } \\ 0 \\ \frac { 3 } { 4 } \end{array} \right]\)
• E) \(\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \\ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } 0 \\ - \frac { 3 } { 8 } \\ 0 \\ - \frac { 3 } { 4 } \end{array} \right]\)