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

question 52

Multiple Choice

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

• A)
• \[
• \left[\begin{array}{cccc}
• \frac{1}{2} & -\frac{1}{3} & 0 & \frac{1}{2} \\
• \frac{1}{6} & -\frac{1}{6} & 0 & \frac{1}{4} \\
• \frac{1}{6} & -\frac{1}{12} & 0 & \frac{1}{6} \\
• 0 & 0 & -\frac{1}{2} & 0
• \end{array}\right]
• B)
• \left[\begin{array}{cccc}
• -1 & 1 & 0 & 3 \\
• \frac{1}{2} & 0 & 0 & -\frac{1}{2} \\
• 0 & -\frac{1}{3} & 0 & -\frac{1}{2} \\
• 0 & 0 & -\frac{1}{2} & 0
• \end{array}\right]
• \]
• C)\[
• \left[\begin{array}{cccc}
• -1 & \frac{1}{2} & 0 & 0 \\
• 1 & 0 & -\frac{1}{3} & 0 \\
• 0 & 0 & 0 & -\frac{1}{2} \\
• 3-\frac{1}{2} & -\frac{1}{2} & 0
• \end{array}\right]
• \]
• D) No inverse

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