Find the inverse of the matrix. $$\left[ \begin{array} { c c c }
1 & 0 & 5 \
1 & 1 & 5 \
- 5 & 1 & 1
\end{array} \right]$$
A) $$\left[ \begin{array} { c c c }
- 29 & 5 & - 5 \
- 1 & 1 & 0 \
6 & 1 & 1
\end{array} \right]$$
B) $$\left[ \begin{array} { c c c }
4 & \frac { 5 } { 26 } & - \frac { 5 } { 26 } \
1 & 1 & 0 \
\frac { 6 } { 26 } & - \frac { 1 } { 26 } & \frac { 1 } { 26 }
\end{array} \right]$$
C) $$\left[ \begin{array} { c c c }
- \frac { 4 } { 26 } & \frac { 5 } { 26 } & - \frac { 5 } { 26 } \
- 1 & 1 & 0 \
\frac { 6 } { 26 } & - \frac { 1 } { 26 } & \frac { 1 } { 26 }
\end{array} \right]$$
D) $$\left[ \begin{array} { c c c }
29 & 5 & - 5 \
- 1 & 1 & - 1 \
6 & - 1 & 1
\end{array} \right]$$
E) $$\left[ \begin{array} { c c c }
29 & 5 & - 5 \
- 1 & 1 & 1 \
6 & - 1 & 1
\end{array} \right]$$

Question

Find the inverse of the matrix.​ $$\left[ \begin{array} { c c c } 
1 & 0 & 5 \
1 & 1 & 5 \
- 5 & 1 & 1
\end{array} \right]$$ ​
A)​​ $$\left[ \begin{array} { c c c } 
- 29 & 5 & - 5 \
- 1 & 1 & 0 \
6 & 1 & 1
\end{array} \right]$$
B) $$\left[ \begin{array} { c c c } 
4 & \frac { 5 } { 26 } & - \frac { 5 } { 26 } \
1 & 1 & 0 \
\frac { 6 } { 26 } & - \frac { 1 } { 26 } & \frac { 1 } { 26 }
\end{array} \right]$$
C)​ $$\left[ \begin{array} { c c c } 
- \frac { 4 } { 26 } & \frac { 5 } { 26 } & - \frac { 5 } { 26 } \
- 1 & 1 & 0 \
\frac { 6 } { 26 } & - \frac { 1 } { 26 } & \frac { 1 } { 26 }
\end{array} \right]$$
D)​ $$\left[ \begin{array} { c c c } 
29 & 5 & - 5 \
- 1 & 1 & - 1 \
6 & - 1 & 1
\end{array} \right]$$
E)​ $$\left[ \begin{array} { c c c } 
29 & 5 & - 5 \
- 1 & 1 & 1 \
6 & - 1 & 1
\end{array} \right]$$

Quizplus · Accepted Answer

To find the inverse of a matrix, we need to use the formula:

inverse = (1/det(A)) * adj(A), where det(A) is the determinant of the matrix and adj(A) is the adjugate (transpose of the matrix of cofactors).

Using this formula, we can calculate that det(A) = -4 and adj(A) =

11ea99db_b312_9bfd_94ac_61aff1200162_TB4590_00.

So the inverse is:

inverse = (-1/4) * 11ea99db_b312_9bfd_94ac_61aff1200162_TB4590_00 =

11ea99db_b312_74eb_94ac_0d8487d46bdf_TB4590_00.

Therefore, the best choice is C.

Find the Inverse of the Matrix [105115−511]\left[ \begin{array} { c c c } 1 & 0 & 5 \\1 & 1 & 5 \\- 5 & 1 & 1\end{array} \right]​11−5​011​551​​

Find the Inverse of the Matrix $\left[ \begin{array} { c c c } 1 & 0 & 5 \\1 & 1 & 5 \\- 5 & 1 & 1\end{array} \right]$