Find the inverse of the matrix $$\left[ \begin{array} { c c c }
7 & 7 & 7 \
21 & 35 & 28 \
21 & 42 & 35
\end{array} \right]$$ .
A) $$\frac { 1 } { 7 } \left[ \begin{array} { c c c }
1 & 1 & - 1 \
- 3 & 2 & - 1 \
3 & - 3 & 2
\end{array} \right]$$
B) $$\frac { 1 } { 7 } \left[ \begin{array} { c c c }
1 & 1 & 1 \
0 & - 2 & - 1 \
3 & - 3 & 2
\end{array} \right]$$
C) $$- 7 \left[ \begin{array} { c c c }
3 & 1 & 0 \
- 3 & 1 & - 1 \
1 & - 3 & 2
\end{array} \right]$$
D) $$- \frac { 1 } { 7 } \left[ \begin{array} { c c c }
1 & 0 & - 1 \
- 3 & 2 & - 1 \
2 & - 3 & 3
\end{array} \right]$$
E) $$7 \left[ \begin{array} { c c c }
1 & 1 & 1 \
- 3 & 0 & - 1 \
3 & - 3 & 2
\end{array} \right]$$

Question

Find the inverse of the matrix $$\left[ \begin{array} { c c c } 
7 & 7 & 7 \
21 & 35 & 28 \
21 & 42 & 35
\end{array} \right]$$ . ​
A)​ $$\frac { 1 } { 7 } \left[ \begin{array} { c c c } 
1 & 1 & - 1 \
- 3 & 2 & - 1 \
3 & - 3 & 2
\end{array} \right]$$
B)​ $$\frac { 1 } { 7 } \left[ \begin{array} { c c c } 
1 & 1 & 1 \
0 & - 2 & - 1 \
3 & - 3 & 2
\end{array} \right]$$
C)​ $$- 7 \left[ \begin{array} { c c c } 
3 & 1 & 0 \
- 3 & 1 & - 1 \
1 & - 3 & 2
\end{array} \right]$$
D)​ $$- \frac { 1 } { 7 } \left[ \begin{array} { c c c } 
1 & 0 & - 1 \
- 3 & 2 & - 1 \
2 & - 3 & 3
\end{array} \right]$$
E)​ $$7 \left[ \begin{array} { c c c } 
1 & 1 & 1 \
- 3 & 0 & - 1 \
3 & - 3 & 2
\end{array} \right]$$

Quizplus · Accepted Answer

The inverse of a matrix can be found using the formula $A^{-1} = \frac{1}{\text{det}(A)} \cdot \text{adj}(A)$, where $\text{det}(A)$ is the determinant of the matrix and $\text{adj}(A)$ is the adjugate of the matrix. For the given matrix, the correct inverse is option A, which indicates that the calculations for the determinant and the adjugate matrix have been correctly applied, leading to the given solution when multiplied by $\frac{1}{7}$.

Find the Inverse of the Matrix [777213528214235]\left[ \begin{array} { c c c } 7 & 7 & 7 \\21 & 35 & 28 \\21 & 42 & 35\end{array} \right]​72121​73542​72835​​

Find the Inverse of the Matrix $\left[ \begin{array} { c c c } 7 & 7 & 7 \\21 & 35 & 28 \\21 & 42 & 35\end{array} \right]$