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)
$\left[ \begin{array} { l } x _ { 1 } \ x _ { 2 } \ x _ { 3 } \ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } 0 \ - \frac { 3 } { 8 } \ 0 \ - \frac { 3 } { 4 } \end{array} \right]$

Question

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)
$\left[ \begin{array} { l } x _ { 1 } \ x _ { 2 } \ x _ { 3 } \ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } 0 \ - \frac { 3 } { 8 } \ 0 \ - \frac { 3 } { 4 } \end{array} \right]$

Quizplus · Accepted Answer

To solve the system of linear equations using the given inverse matrix, we multiply the inverse matrix by the constants on the right side of the equations. The correct solution is obtained by performing this matrix multiplication correctly, which results in the solution vector given in option A.

Solve the System of Linear Equations Using the Inverse Matrix