Find inverse of the matrix. $$\left[ \begin{array} { l l l }
2 & 2 & 0 \
0 & 2 & 0 \
1 & 0 & 1
\end{array} \right]$$
A) $\left[ \begin{array} { c c c }
2 & - 2 & 0 \
0 & 2 & 0 \
- 2 & 1 / 2 & 1
\end{array} \right]$
B) $\left[ \begin{array} { c c c }
2 & - 1 / 2 & 0 \
1 & 2 & 0 \
- 2 & 1 / 2 & 1
\end{array} \right]$
C) $\left[ \begin{array} { c c c }
1 & - 1 & 1 \
0 & 1 / 2 & 0 \
- 1 & 1 / 2 & 1
\end{array} \right]$
D) $\left[ \begin{array} { c c c }
1 / 2 & - 1 / 2 & 0 \
0 & 1 / 2 & 0 \
- 1 / 2 & 1 / 2 & 1
\end{array} \right]$

E) none

Question

Find inverse of the matrix. $$\left[ \begin{array} { l l l } 
2 & 2 & 0 \
0 & 2 & 0 \
1 & 0 & 1
\end{array} \right]$$
A) $\left[ \begin{array} { c c c } 
2 & - 2 & 0 \
0 & 2 & 0 \
- 2 & 1 / 2 & 1
\end{array} \right]$
B) $\left[ \begin{array} { c c c } 
2 & - 1 / 2 & 0 \
1 & 2 & 0 \
- 2 & 1 / 2 & 1
\end{array} \right]$
C) $\left[ \begin{array} { c c c } 
1 & - 1 & 1 \
0 & 1 / 2 & 0 \
- 1 & 1 / 2 & 1
\end{array} \right]$
D) $\left[ \begin{array} { c c c } 
1 / 2 & - 1 / 2 & 0 \
0 & 1 / 2 & 0 \
- 1 / 2 & 1 / 2 & 1
\end{array} \right]$

E) none

Quizplus · Accepted Answer

To find the inverse of a matrix, we can use the formula $A^{-1} = \frac{1}{\text{det}(A)} \cdot \text{adj}(A)$, where $\text{det}(A)$ is the determinant of the matrix $A$ and $\text{adj}(A)$ is the adjugate of $A$. For the given matrix, the determinant can be calculated as $2(2*1 - 0*0) - 2(0*1 - 0*1) + 0(0*0 - 2*1) = 4$. The adjugate matrix is found by taking the transpose of the cofactor matrix. After calculating the cofactors and taking their transpose, we get the adjugate matrix. Dividing each element of the adjugate matrix by the determinant (4) gives us the inverse matrix. The correct inverse matrix is option D, which matches the calculation process.

Find Inverse of the Matrix [220020101]\left[ \begin{array} { l l l } 2 & 2 & 0 \\0 & 2 & 0 \\1 & 0 & 1\end{array} \right]​201​220​001​​

Find Inverse of the Matrix $\left[ \begin{array} { l l l } 2 & 2 & 0 \\0 & 2 & 0 \\1 & 0 & 1\end{array} \right]$