Solve {cc}{1/3}&{1/3}{1/12}&{-5/6}

$$\left| \begin{array} { c c } { \frac { 1 } { 3 } } & { \frac { 1 } { 3 } } \\ { \frac { 1 } { 12 } } & { - \frac { 5 } { 6 } } \end{array} \right|$$

Evaluate

$$-\frac{11}{36}\approx -0.305555556$$

Steps Using Diagonal Rule

Find the determinant of the matrix.

$$det(\left(\begin{matrix}\frac{1}{3}&\frac{1}{3}\\\frac{1}{12}&-\frac{5}{6}\end{matrix}\right))$$

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

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

Multiply \frac{1}{3} times -\frac{5}{6} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$-\frac{5}{18}-\frac{1}{3}\times \frac{1}{12}$$

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

$$-\frac{5}{18}-\frac{1}{36}$$

Subtract \frac{1}{36} from -\frac{5}{18} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$-\frac{11}{36}$$

Factor

$$-\frac{11}{36} = -0.3055555555555556$$