Find the inverse, if it exists, for the matrix.
-$\left[ \begin{array} { l l } 3 & 0 \ 3 & 4 \end{array} \right]$
A) The inverse does not exist.
B)
$$\left[ \begin{array} { r r }
\frac { 1 } { 3 } & 0 \
- \frac { 1 } { 4 } & \frac { 1 } { 4 }
\end{array} \right]$$
C)
$$\left[ \begin{array} { c c }
\frac { 1 } { 4 } & 0 \
- \frac { 1 } { 4 } & \frac { 1 } { 3 }
\end{array} \right]$$
D)
$$\left[ \begin{array} { l l }
\frac { 1 } { 3 } & 0 \
\frac { 1 } { 4 } & \frac { 1 } { 4 }
\end{array} \right]$$

Question

Find the inverse, if it exists, for the matrix.
-$\left[ \begin{array} { l l } 3 & 0 \ 3 & 4 \end{array} \right]$
A) The inverse does not exist.
B)
$$\left[ \begin{array} { r r } 
\frac { 1 } { 3 } & 0 \
- \frac { 1 } { 4 } & \frac { 1 } { 4 }
\end{array} \right]$$
C)
$$\left[ \begin{array} { c c } 
\frac { 1 } { 4 } & 0 \
- \frac { 1 } { 4 } & \frac { 1 } { 3 }
\end{array} \right]$$
D)
$$\left[ \begin{array} { l l } 
\frac { 1 } { 3 } & 0 \
\frac { 1 } { 4 } & \frac { 1 } { 4 }
\end{array} \right]$$

Quizplus · Accepted Answer

The determinant of the matrix is $3 \times 4 - 0 \times 3 = 12$, which is not zero, so the inverse exists. The formula for the inverse of a 2x2 matrix $\left[ \begin{array} { l l } a & b \ c & d \end{array} \right]$ is $\frac{1}{ad-bc}\left[ \begin{array} { r r } d & -b \ -c & a \end{array} \right]$. Applying this formula to the given matrix yields the matrix in option B.

Find the Inverse, If It Exists, for the Matrix [3034]\left[ \begin{array} { l l } 3 & 0 \\ 3 & 4 \end{array} \right][33​04​]

Find the Inverse, If It Exists, for the Matrix $\left[ \begin{array} { l l } 3 & 0 \\ 3 & 4 \end{array} \right]$