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:

Accounting Equation

A fundamental principle in finance that states assets equal liabilities plus equity.

Note Settlement

The process of fulfilling the obligations of a promissory note, typically involving the payment of the principal and accrued interest.

Past Due Account

An account receivable that has not been paid by the due date, typically subject to late fees or other penalties until settled.

Accounting Equation

A fundamental principle of accounting representing the relationship between assets, liabilities, and owner's equity: Assets = Liabilities + Owner's Equity.