Solve the System of Linear Equations Using the Inverse Matrix

question 12

Multiple Choice

Solve the system of linear equations
$\left\{ \begin{array} { l } 6 x _ { 1 } - 12 x _ { 2 } - 6 x _ { 3 } - 12 x _ { 4 } = 0 \\18 x _ { 1 } - 30 x _ { 2 } - 12 x _ { 3 } - 18 x _ { 4 } = - 3 \\12 x _ { 1 } - 30 x _ { 2 } - 12 x _ { 3 } - 30 x _ { 4 } = 2 \\- 6 x _ { 1 } + 24 x _ { 2 } + 24 x _ { 3 } + 66 x _ { 4 } = 0\end{array} \right.$
using the inverse matrix $\frac { 1 } { 6 } \left[ \begin{array} { c c c c } - 24 & 7 & 1 & - 2 \\ - 10 & 3 & 0 & - 1 \\ - 29 & 7 & 3 & - 2 \\ 12 & - 3 & - 1 & 1 \end{array} \right]$ .

• A) \(\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \\ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } - \frac { 19 } { 6 } \\ - \frac { 3 } { 2 } \\ - \frac { 5 } { 2 } \\ \frac { 7 } { 6 } \end{array} \right]\)
• B) \(\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \\ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } - \frac { 7 } { 6 } \\ - \frac { 5 } { 6 } \\ \frac { 3 } { 2 } \\ - \frac { 3 } { 2 } \end{array} \right]\)
• C) \(\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \\ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } - \frac { 3 } { 2 } \\ - \frac { 19 } { 6 } \\ 0 \\ \frac { 7 } { 6 } \end{array} \right]\)
• D)
• \(\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \\ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } - \frac { 1 } { 2 } \\ \frac { 1 } { 6 } \\ 0 \\ \frac { 1 } { 3 } \end{array} \right]\)
• E) \(\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \\ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } 0 \\ - \frac { 1 } { 6 } \\ 0 \\ - \frac { 1 } { 3 } \end{array} \right]\)

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Definitions:

Cerebral Hemispheres

The two halves of the brain, divided into left and right sides, responsible for controlling different functions and cognitive processes.

Commissural Fibers

Axonal connections between the hemispheres of the brain, facilitating communication.

Hemispheres

The two halves of the brain, each specializing in different functions but working together to process information.

White Matter

Brain tissue composed of myelinated nerve fibers (axons) that connect different brain areas and transmit nerve impulses.