Find the inverse of the matrix. $$\left[ \begin{array} { l l }
4 & 1 \
1 & 4
\end{array} \right]$$
A) $$\left[ \begin{array} { c c }
\frac { 4 } { 15 } & \frac { 1 } { 15 } \\
\frac { 1 } { 15 } & \frac { 4 } { 15 }
\end{array} \right]$$
B) $$\left[ \begin{array} { l }
- \frac { 4 } { 15 } - \frac { 1 } { 15 } \
- \frac { 1 } { 15 } - \frac { 4 } { 15 }
\end{array} \right]$$
C) $$\left[ \begin{array} { c c }
\frac { 4 } { 15 } & - \frac { 1 } { 15 } \
- \frac { 1 } { 15 } & \frac { 4 } { 15 }
\end{array} \right.$$
D) $$\left[ \begin{array} { c c }
- \frac { 4 } { 15 } & \frac { 1 } { 15 } \
\frac { 1 } { 15 } & - \frac { 4 } { 15 }
\end{array} \right]$$
E) $$\left[ \begin{array} { c c }
\frac { 4 } { 15 } & 0 \
0 & \frac { 4 } { 15 }
\end{array} \right]$$

Question

Find the inverse of the matrix.​ $$\left[ \begin{array} { l l } 
4 & 1 \
1 & 4
\end{array} \right]$$ ​
A)​​ $$\left[ \begin{array} { c c } 
\frac { 4 } { 15 } & \frac { 1 } { 15 } \\
\frac { 1 } { 15 } & \frac { 4 } { 15 }
\end{array} \right]$$
B)​ $$\left[ \begin{array} { l } 
- \frac { 4 } { 15 } - \frac { 1 } { 15 } \
- \frac { 1 } { 15 } - \frac { 4 } { 15 }
\end{array} \right]$$
C)​ $$\left[ \begin{array} { c c } 
\frac { 4 } { 15 } & - \frac { 1 } { 15 } \
- \frac { 1 } { 15 } & \frac { 4 } { 15 }
\end{array} \right.$$
D)​ $$\left[ \begin{array} { c c } 
- \frac { 4 } { 15 } & \frac { 1 } { 15 } \
\frac { 1 } { 15 } & - \frac { 4 } { 15 }
\end{array} \right]$$ ​
E)​ $$\left[ \begin{array} { c c } 
\frac { 4 } { 15 } & 0 \
0 & \frac { 4 } { 15 }
\end{array} \right]$$

Quizplus · Accepted Answer

To find the inverse of a matrix, we need to use the formula: 
Inverse of A = 1/det(A) * adj(A) 
where det(A) is the determinant of the matrix A and adj(A) is the adjugate of the matrix A.

Using this formula, we can find that: 
det(A) = -1 
adj(A) = 
[ -94ac -7901 51ee ]
[ 0      a013  0    ]
[ 0     -b310  0    ]

Therefore, the inverse of the matrix is: 
1/det(A) * adj(A) = 
[ 94ac+7901    -51ee    ]
[ 0            1/a013  ]
[ 0           b310    ]

So the correct answer is C.

Find the Inverse of the Matrix [4114]\left[ \begin{array} { l l } 4 & 1 \\1 & 4\end{array} \right][41​14​]

Find the Inverse of the Matrix $\left[ \begin{array} { l l } 4 & 1 \\1 & 4\end{array} \right]$