Find the Inverse, If It Exists, for the Matrix $$\left[ \begin{array} { r r r r } 0 & 5 & 0 & - 3 \\4 & 15 & - 3 & - 6 \\8 & 10 & - 6 & - 3 \\12 & 0 & - 6 & 0\end{array} \right]$$

Find the inverse, if it exists, for the matrix.
- $$\left[ \begin{array} { r r r r } 0 & 5 & 0 & - 3 \\4 & 15 & - 3 & - 6 \\8 & 10 & - 6 & - 3 \\12 & 0 & - 6 & 0\end{array} \right]$$

A)
$$\left[ \begin{array} { r r r r } \frac { 1 } { 2 } & - \frac { 1 } { 2 } & \frac { 1 } { 2 } & - \frac { 1 } { 4 } \\\frac { 3 } { 5 } & - \frac { 2 } { 5 } & \frac { 1 } { 5 } & 0 \\1 & - 1 & 1 & \frac { 1 } { 3 } \\- 1 & - \frac { 2 } { 3 } & \frac { 1 } { 3 } & 0\end{array} \right]$$

B) The inverse does not exist.

C)
$$\left[ \begin{array} { r r r r } - \frac { 1 } { 2 } & - \frac { 3 } { 5 } & - 1 & - \frac { 4 } { 3 } \\\frac { 1 } { 2 } & \frac { 2 } { 5 } & 1 & \frac { 1 } { 3 } \\- \frac { 1 } { 2 } & - \frac { 1 } { 5 } & - 1 & - \frac { 1 } { 3 } \\\frac { 1 } { 4 } & 0 & \frac { 1 } { 3 } & 0\end{array} \right]$$

D)

$$\left[ \begin{array} { c c c c } - \frac { 1 } { 2 } & \frac { 1 } { 2 } & - \frac { 1 } { 2 } & \frac { 1 } { 4 } \\- \frac { 3 } { 5 } & \frac { 2 } { 5 } & - \frac { 1 } { 5 } & 0 \\- 1 & 1 & - 1 & \frac { 1 } { 3 } \\- \frac { 4 } { 3 } & \frac { 2 } { 3 } & - \frac { 1 } { 3 } & 0\end{array} \right]$$

Correct Answer:

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