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

Question

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

Quizplus · Accepted Answer

The matrix has a row of zeros in its reduced row echelon form, indicating it is singular and does not have an inverse.

Find the Inverse, If It Exists, for the Matrix [5−56−25−4−2−110−94−30−10120]\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]​55100​−5−4−9−10​6−2412​−2−1−30​​

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