Find the Inverse, If It Exists, for the Matrix $$\left[ \begin{array} { r r r r } 5 & - 5 & 6 & - 2 \\5 & - 4 & - 2 & - 1 \\10 & - 9 & 4 & - 3 \\0 & - 10 & 12 & 0\end{array} \right]$$

question 37

Multiple Choice

Find the inverse, if it exists, for the matrix.
- $$\left[ \begin{array} { r r r r } 5 & - 5 & 6 & - 2 \\5 & - 4 & - 2 & - 1 \\10 & - 9 & 4 & - 3 \\0 & - 10 & 12 & 0\end{array} \right]$$

• A)
• \[\left[ \begin{array} { r r r r }
• 1 & 0 & 0 & - \frac { 2 } { 5 } \\
• 0 & 1 & 0 & - \frac { 3 } { 17 } \\
• 0 & 0 & 1 & - \frac { 5 } { 34 } \\
• 0 & 0 & 0 & 0
• \end{array} \right]\]
• B)
• \[\left[ \begin{array} { c c c c }
• \frac { 1 } { 5 } & - \frac { 1 } { 5 } & \frac { 1 } { 6 } & - \frac { 1 } { 2 } \\
• \frac { 1 } { 5 } & - \frac { 1 } { 4 } & - 2 & - 1 \\
• \frac { 1 } { 10 } & - \frac { 1 } { 9 } & \frac { 1 } { 4 } & - \frac { 1 } { 3 } \\
• 0 & - \frac { 1 } { 10 } & \frac { 1 } { 12 } & 0
• \end{array} \right]\]
• C) The inverse does not exist.
• D)
• \[\left[ \begin{array} { c c c c }
• \frac { 1 } { 5 } & - \frac { 1 } { 5 } & \frac { 1 } { 6 } & - \frac { 1 } { 2 } \\
• \frac { 1 } { 5 } & - \frac { 1 } { 4 } & - \frac { 1 } { 2 } & - 1 \\
• \frac { 1 } { 10 } & - \frac { 1 } { 9 } & \frac { 1 } { 4 } & - \frac { 1 } { 3 } \\
• 0 & - \frac { 1 } { 10 } & \frac { 1 } { 12 } & 0
• \end{array} \right]\]

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