Solve Matrix

$$\left| \begin{array} { l l } { \frac { 1 } { 2 } } & { \frac { 1 } { 12 } } \\ { - 2 / 3 } & { - \frac { 5 } { 3 } } \end{array} \right|$$

Evaluate

$$-\frac{7}{9}\approx -0.777777778$$

Steps Using Diagonal Rule

Find the determinant of the matrix.

$$det(\left(\begin{matrix}\frac{1}{2}&\frac{1}{12}\\-\frac{2}{3}&-\frac{5}{3}\end{matrix}\right))$$

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

$$\frac{1}{2}\left(-\frac{5}{3}\right)-\frac{1}{12}\left(-\frac{2}{3}\right)$$

Multiply \frac{1}{2} times -\frac{5}{3} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$-\frac{5}{6}-\frac{1}{12}\left(-\frac{2}{3}\right)$$

Multiply \frac{1}{12} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$-\frac{5}{6}-\left(-\frac{1}{18}\right)$$

Subtract -\frac{1}{18} from -\frac{5}{6} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$-\frac{7}{9}$$

Factor

$$-\frac{7}{9} = -0.7777777777777778$$