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

question 172

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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