Find the inverse, if it exists, for the matrix.
-$$\left[ \begin{array} { r r }
- 3 & 4 \
6 & - 4
\end{array} \right]$$
A)
$\left[ \begin{array} { l } \frac { 1 } { 3 } \frac { 1 } { 3 } \ \frac { 1 } { 2 } \frac { 1 } { 4 } \end{array} \right]$
B)
$\left[ \begin{array} { l l } \frac { 1 } { 2 } & \frac { 1 } { 4 } \ \frac { 1 } { 3 } & \frac { 1 } { 3 } \end{array} \right]$
C)
$\left[\begin{array}{ll}
\frac{1}{4} & \frac{1}{3} \
\frac{1}{2} & \frac{1}{3}
\end{array}\right]$
D)
$\left[\begin{array}{c}
\frac{1}{3}-\frac{1}{3} \
-\frac{1}{2}-\frac{1}{4}
\end{array}\right]$

Question

Find the inverse, if it exists, for the matrix.
-$$\left[ \begin{array} { r r } 
- 3 & 4 \
6 & - 4
\end{array} \right]$$
A)
$\left[ \begin{array} { l } \frac { 1 } { 3 } \frac { 1 } { 3 } \ \frac { 1 } { 2 } \frac { 1 } { 4 } \end{array} \right]$
B)
$\left[ \begin{array} { l l } \frac { 1 } { 2 } & \frac { 1 } { 4 } \ \frac { 1 } { 3 } & \frac { 1 } { 3 } \end{array} \right]$
C)
$\left[\begin{array}{ll}
\frac{1}{4} & \frac{1}{3} \
\frac{1}{2} & \frac{1}{3}
\end{array}\right]$
D)
$\left[\begin{array}{c}
\frac{1}{3}-\frac{1}{3} \
-\frac{1}{2}-\frac{1}{4}
\end{array}\right]$

Quizplus · Accepted Answer

The inverse of a matrix is found by dividing the adjoint of the matrix by the determinant of the matrix. The adjoint of a matrix is the transpose of the cofactor matrix of the matrix. The cofactor matrix is found by replacing each element of the matrix with the determinant of the submatrix formed by deleting the row and column of the element. The determinant of a matrix is the sum of the products of the elements in each row or column of the matrix multiplied by their respective cofactors.For the given matrix, the adjoint is:$$\left[ \begin{array} { r r } -4 & -4 \-6 & -3\end{array} ight]$$And the determinant is:$$(-3)(-4) - (4)(6) = 12 - 24 = -12$$Therefore, the inverse of the matrix is:$$\left[ \begin{array} { r r } -4 & -4 \-6 & -3\end{array} ight] / -12 = \left[ \begin{array} { l } \frac { 1 } { 3 } \frac { 1 } { 3 } \ \frac { 1 } { 2 } \frac { 1 } { 4 } \end{array} ight]$$

Find the Inverse, If It Exists, for the Matrix [−346−4]\left[ \begin{array} { r r } - 3 & 4 \\6 & - 4\end{array} \right][−36​4−4​]

Find the Inverse, If It Exists, for the Matrix $\left[ \begin{array} { r r } - 3 & 4 \\6 & - 4\end{array} \right]$