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

question 235

Multiple Choice

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

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

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