Find the Inverse, If It Exists, for the Matrix $$\left[ \begin{array} { r r r r } 4 & - 2 & 0 & 3 \\12 & - 4 & 0 & 6 \\6 & - 8 & 0 & 9 \\0 & 0 & - 6 & 0\end{array} \right]$$

Find the inverse, if it exists, for the matrix.
- $$\left[ \begin{array} { r r r r } 4 & - 2 & 0 & 3 \\12 & - 4 & 0 & 6 \\6 & - 8 & 0 & 9 \\0 & 0 & - 6 & 0\end{array} \right]$$

A) The inverse does not exist.
B)
$$\left[ \begin{array} { r r r r } - \frac { 1 } { 2 } & 3 & 0 & 3 \\\frac { 1 } { 4 } & - \frac { 3 } { 4 } & 0 & - \frac { 5 } { 6 } \\0 & - \frac { 1 } { 2 } & 0 & - \frac { 1 } { 3 } \\0 & 0 & - \frac { 1 } { 6 } & 0\end{array} \right]$$
C)
$$\left[ \begin{array} { r r r r } - \frac { 1 } { 2 } & \frac { 1 } { 4 } & 0 & 0 \\3 & - \frac { 3 } { 4 } & - \frac { 1 } { 2 } & 0 \\0 & 0 & 0 & - \frac { 1 } { 6 } \\3 & - \frac { 5 } { 6 } & - \frac { 1 } { 3 } & 0\end{array} \right]$$
D)
$$\left[ \begin{array} { c c c c } \frac { 1 } { 4 } & - \frac { 1 } { 2 } & 0 & \frac { 1 } { 3 } \\\frac { 1 } { 12 } & - \frac { 1 } { 4 } & 0 & \frac { 1 } { 6 } \\\frac { 1 } { 6 } & - \frac { 1 } { 8 } & 0 & \frac { 1 } { 9 } \\0 & 0 & - \frac { 1 } { 6 } & 0\end{array} \right]$$

Correct Answer:

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