Solve {rr}{1/5}&{-1/4}{-1/3}&{1/3}

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

Evaluate

$$-\frac{1}{60}\approx -0.016666667$$

Steps Using Diagonal Rule

Find the determinant of the matrix.

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

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

$$\frac{1}{5}\times \frac{1}{3}-\left(-\frac{1}{4}\left(-\frac{1}{3}\right)\right)$$

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

$$\frac{1}{15}-\left(-\frac{1}{4}\left(-\frac{1}{3}\right)\right)$$

Multiply -\frac{1}{4} times -\frac{1}{3} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$\frac{1}{15}-\frac{1}{12}$$

Subtract \frac{1}{12} from \frac{1}{15} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$-\frac{1}{60}$$

Factor

$$-\frac{1}{60} = -0.016666666666666666$$