Solve Matrix

$$\left( \begin{array} { l l } { \frac { 2 } { 3 } } & { 3 } \\ { 3 } & { 4 } \end{array} \right)$$

Calculate Determinant

$$-\frac{19}{3} = -6\frac{1}{3} = -6.333333333333333$$

Steps Using Diagonal Rule

Find the determinant of the matrix.

$$det(\left(\begin{matrix}\frac{2}{3}&3\\3&4\end{matrix}\right))$$

For the 2\times 2 matrix \left(\begin{matrix}a&b\\c&d\end{matrix}\right), the determinant is ad-bc.

$$\frac{2}{3}\times 4-3\times 3$$

Multiply \frac{2}{3} times 4.

$$\frac{8}{3}-3\times 3$$

Multiply 3 times 3.

$$\frac{8}{3}-9$$

Subtract 9 from \frac{8}{3}.

$$-\frac{19}{3}$$

Evaluate

$$\left(\begin{matrix}\frac{2}{3}&3\\3&4\end{matrix}\right)$$