​Write the System of Linear Equations as a Matrix Equation $[ A \mid B ]$

question 30

Multiple Choice

​Write the system of linear equations as a matrix equation AX = B,and use Gauss-Jordan elimination on the augmented matrix $[ A \mid B ]$ to solve for the matrix X. $$\left\{ \begin{array} { r l c } x _ { 1 } - x _ { 2 } - 3 x _ { 3 } & = & 6 \\8 x _ { 1 } - 7 x _ { 2 } + 8 x _ { 3 } & = & - 104 \\6 x _ { 1 } - 6 x _ { 2 } - 8 x _ { 3 } & = & - 14\end{array} \right.$$

• A)​ \[\left[ \begin{array} { c c c }
• 1 & - 1 & - 3 \\
• 8 & - 7 & 8 \\
• 6 & - 6 & - 8
• \end{array} \right] = \left[ \begin{array} { c }
• 6 \\
• - 104 \\
• - 14
• \end{array} \right]\]
• B)​ \[\left[ \begin{array} { c c c }
• 1 & - 1 & - 3 \\
• 8 & - 7 & 8 \\
• 6 & - 6 & - 8
• \end{array} \right] \left[ \begin{array} { c }
• - 1 \\
• 8 \\
• - 5
• \end{array} \right] = \left[ \begin{array} { c }
• 6 \\
• 8 \\
• - 5
• \end{array} \right]\]
• C)​ \[\left[ \begin{array} { c c c }
• 1 & - 1 & - 3 \\
• 8 & - 7 & 8 \\
• 6 & - 6 & - 8
• \end{array} \right] \left[ \begin{array} { c }
• 6 \\
• - 1 \\
• - 14
• \end{array} \right] = \left[ \begin{array} { c }
• - 104 \\
• 8 \\
• - 5
• \end{array} \right]\]
• D)​ \[\left[ \begin{array} { c c c }
• 1 & - 1 & - 3 \\
• 8 & - 7 & 8 \\
• 6 & - 6 & - 8
• \end{array} \right] \left[ \begin{array} { c }
• - 1 \\
• 8 \\
• - 5
• \end{array} \right] = \left[ \begin{array} { c }
• 6 \\
• - 104 \\
• - 14
• \end{array} \right]\]
• E)​ \[\left[ \begin{array} { c c c }
• 1 & - 1 & - 3 \\
• 8 & - 7 & 8 \\
• 6 & - 6 & - 8
• \end{array} \right] \left[ \begin{array} { c }
• 6 \\
• - 104 \\
• - 14
• \end{array} \right] = \left[ \begin{array} { c }
• - 1 \\
• 8 \\
• - 5
• \end{array} \right]\]

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Definitions:

Faulty Cause

A logical fallacy that occurs when an incorrect cause is identified for an effect, leading to flawed reasoning.

Qualifiers

Words or phrases that alter or refine the meaning of other words, often indicating aspects such as intensity or degree.

Multiple-Choice Test

A form of assessment where respondents select the best answer from several options presented.

Qualifiers

Words or phrases used to add nuance, limit, or modify the strength of a statement, such as "probably," "mostly," or "in most cases."