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

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)
$$\left[ \begin{array} { c c c c } \frac { 1 } { 5 } & - \frac { 1 } { 5 } & \frac { 1 } { 6 } & - \frac { 1 } { 2 } \\\frac { 1 } { 5 } & - \frac { 1 } { 4 } & - \frac { 1 } { 2 } & - 1 \\\frac { 1 } { 10 } & - \frac { 1 } { 9 } & \frac { 1 } { 4 } & - \frac { 1 } { 3 } \\0 & - \frac { 1 } { 10 } & \frac { 1 } { 12 } & 0\end{array} \right]$$

Correct Answer:

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