Find the inverse of the matrix (if it exists). $$\left[ \begin{array} { c c c }
4 & 0 & 0 \
6 & 0 & 0 \
5 & 11 & 11
\end{array} \right]$$
A) $$\left[ \begin{array} { c c c }
- 4 & 0 & 0 \
- 6 & 0 & 0 \
5 & 4 & 11
\end{array} \right]$$
B) $$\left[ \begin{array} { c c c }
- 4 & 0 & 0 \
- 6 & 0 & 0 \
- 5 & - 4 & - 11
\end{array} \right]$$
C) $$\left[ \begin{array} { c c c }
4 & 0 & 0 \
6 & 0 & 0 \
5 & 4 & 11
\end{array} \right]$$
D) $$\left[ \begin{array} { c c c }
- 4 & 0 & 0 \
- 6 & 0 & 0 \
- 5 & 4 & 11
\end{array} \right]$$
E)Does not exist

Question

Find the inverse of the matrix (if it exists).​ $$\left[ \begin{array} { c c c } 
4 & 0 & 0 \
6 & 0 & 0 \
5 & 11 & 11
\end{array} \right]$$ ​
A)​ $$\left[ \begin{array} { c c c } 
- 4 & 0 & 0 \
- 6 & 0 & 0 \
5 & 4 & 11
\end{array} \right]$$
B)​ $$\left[ \begin{array} { c c c } 
- 4 & 0 & 0 \
- 6 & 0 & 0 \
- 5 & - 4 & - 11
\end{array} \right]$$
C)​ $$\left[ \begin{array} { c c c } 
4 & 0 & 0 \
6 & 0 & 0 \
5 & 4 & 11
\end{array} \right]$$
D)​ $$\left[ \begin{array} { c c c } 
- 4 & 0 & 0 \
- 6 & 0 & 0 \
- 5 & 4 & 11
\end{array} \right]$$
E)Does not exist

Quizplus · Accepted Answer

The inverse of a matrix exists only if the determinant of the matrix is not zero. However, the given matrix has a determinant of zero (can be calculated using any method like row reduction, cofactor expansion, etc.). Hence, the inverse of this matrix does not exist.

Find the Inverse of the Matrix (If It Exists) [40060051111]\left[ \begin{array} { c c c } 4 & 0 & 0 \\6 & 0 & 0 \\5 & 11 & 11\end{array} \right]​465​0011​0011​​

Find the Inverse of the Matrix (If It Exists) $\left[ \begin{array} { c c c } 4 & 0 & 0 \\6 & 0 & 0 \\5 & 11 & 11\end{array} \right]$