Use Row Reduction to Find the Inverse of the Given $\left[ \begin{array} { c c c } 1 & 4 & - 1 \\4 & 5 & - 4 \\- 1 & 4 & 5\end{array} \right]$

question 142

Multiple Choice

Use row reduction to find the inverse of the given matrix, if it exists, and check your answer by multiplication. $\left[ \begin{array} { c c c } 1 & 4 & - 1 \\4 & 5 & - 4 \\- 1 & 4 & 5\end{array} \right]$

• A) \(\left[ \begin{array} { c c c }
• - \frac { 41 } { 44 } & \frac { 6 } { 11 } & \frac { 1 } { 4 } \\
• \frac { 4 } { 11 } & - \frac { 1 } { 11 } & 0 \\
• - \frac { 21 } { 44 } & \frac { 2 } { 11 } & \frac { 1 } { 4 }
• \end{array} \right]\)
• B) \(\left[ \begin{array} { c c c }
• - \frac { 25 } { 26 } & \frac { 4 } { 13 } & \frac { 19 } { 26 } \\
• \frac { 8 } { 13 } & - \frac { 1 } { 13 } & \frac { 4 } { 13 } \\
• - \frac { 1 } { 2 } & 0 & \frac { 1 } { 2 }
• \end{array} \right]\)
• C) \(\left[ \begin{array} { c c c }
• - \frac { 41 } { 44 } & \frac { 4 } { 11 } & \frac { 21 } { 44 } \\
• \frac { 6 } { 11 } & - \frac { 1 } { 11 } & \frac { 2 } { 11 } \\
• - \frac { 1 } { 4 } & 0 & \frac { 1 } { 4 }
• \end{array} \right]\)
• D) \(\left[ \begin{array} { c c c }
• - \frac { 25 } { 26 } & \frac { 8 } { 13 } & \frac { 1 } { 2 } \\
• \frac { 4 } { 13 } & - \frac { 1 } { 13 } & 0 \\
• - \frac { 19 } { 26 } & \frac { 4 } { 13 } & \frac { 1 } { 2 }
• \end{array} \right]\)
• E) The inverse matrix does not exist.

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