Solve Matrix

$$\left| \begin{array} { l l } { \frac { 1 } { 2 } } & { 1 } \\ { \frac { 3 } { 4 } } & { \frac { 1 } { 5 } } \end{array} \right|$$

Evaluate

$$-\frac{13}{20}=-0.65$$

Steps Using Diagonal Rule

Find the determinant of the matrix.

$$det(\left(\begin{matrix}\frac{1}{2}&1\\\frac{3}{4}&\frac{1}{5}\end{matrix}\right))$$

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

$$\frac{1}{2}\times \frac{1}{5}-\frac{3}{4}$$

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

$$\frac{1}{10}-\frac{3}{4}$$

Subtract \frac{3}{4} from \frac{1}{10} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$-\frac{13}{20}$$

Factor

$$-\frac{13}{20} = -0.65$$