Find the Inverse, If It Exists, for the Matrix $$\left[ \begin{array} { r r r r } 2 & - 4 & 0 & 2 \\6 & - 8 & 0 & 4 \\6 & - 16 & 0 & 6 \\0 & 0 & - 5 & 0\end{array} \right]$$

Find the inverse, if it exists, for the matrix.
- $$\left[ \begin{array} { r r r r } 2 & - 4 & 0 & 2 \\6 & - 8 & 0 & 4 \\6 & - 16 & 0 & 6 \\0 & 0 & - 5 & 0\end{array} \right]$$

A)
$$\left[ \begin{array} { r r r r } - 1 & \frac { 3 } { 4 } & 0 & 3 \\\frac { 1 } { 2 } & 0 & 0 & - \frac { 1 } { 2 } \\0 & - \frac { 1 } { 4 } & 0 & - \frac { 1 } { 2 } \\0 & 0 & - \frac { 1 } { 5 } & 0\end{array} \right]$$
B)
$$\left[ \begin{array} { r r r r } - 1 & \frac { 1 } { 2 } & 0 & 0 \\\frac { 3 } { 4 } & 0 & - \frac { 1 } { 4 } & 0 \\0 & 0 & 0 & - \frac { 1 } { 5 } \\3 - \frac { 1 } { 2 } & - \frac { 1 } { 2 } & 0\end{array} \right]$$
C)
$$\left[ \begin{array} { c c c c } \frac { 1 } { 2 } & - \frac { 1 } { 4 } & 0 & \frac { 1 } { 2 } \\\frac { 1 } { 6 } & - \frac { 1 } { 8 } & 0 & \frac { 1 } { 4 } \\\frac { 1 } { 6 } & - \frac { 1 } { 16 } & 0 & \frac { 1 } { 6 } \\0 & 0 & - \frac { 1 } { 5 } & 0\end{array} \right]$$
D)
$\text { The inverse does not exist. }$

Correct Answer:

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