Use Row Reduction to Find the Inverse of the Given $\left[ \begin{array} { c c c c } 1 & 1 & - 1 & 1 \\- 3 & 1 & 1 & 0 \\- 3 & 1 & 0 & 1 \\8 & - 1 & - 1 & - 1\end{array} \right]$

question 61

Multiple Choice

Use row reduction to find the inverse of the given matrix, if it exists, and check your answer by multiplication. $\left[ \begin{array} { c c c c } 1 & 1 & - 1 & 1 \\- 3 & 1 & 1 & 0 \\- 3 & 1 & 0 & 1 \\8 & - 1 & - 1 & - 1\end{array} \right]$

• A) \(\left[ \begin{array} { c c c c }
• 2 & - 1 & 5 & 5 \\
• 3 & - 2 & 9 & - 1 \\
• - 4 & 3 & - 11 & - 10 \\
• 1 & - 1 & 3 & 3
• \end{array} \right]\)
• B) \(\left[ \begin{array} { c c c c }
• 2 & 3 & - 4 & 1 \\
• - 1 & - 2 & 3 & - 1 \\
• 5 & 9 & - 11 & 3 \\
• 5 & 8 & - 10 & 3
• \end{array} \right]\)
• C) \(\left[ \begin{array} { c c c c }
• - 1 & 0 & 2 & 1 \\
• 2 & 1 & - 3 & - 1 \\
• - 5 & 0 & 9 & 4 \\
• - 5 & - 1 & 10 & 4
• \end{array} \right]\)
• D) \(\left[ \begin{array} { c c c c }
• - 1 & 2 & - 5 & - 5 \\
• 0 & 1 & 0 & - 1 \\
• 2 & - 3 & 9 & 10 \\
• 1 & - 1 & 4 & 4
• \end{array} \right]\)
• E) The inverse matrix does not exist.

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