Solve {cc}{1408/3}&{19/3}{1099/2}&{11/2}

$$\left| \begin{array} { c c } { \frac { 1408 } { 3 } } & { \frac { 19 } { 3 } } \\ { \frac { 1099 } { 2 } } & { \frac { 11 } { 2 } } \end{array} \right|$$

Evaluate

$$-\frac{5393}{6}\approx -898.833333333$$

Steps Using Diagonal Rule

Find the determinant of the matrix.

$$det(\left(\begin{matrix}\frac{1408}{3}&\frac{19}{3}\\\frac{1099}{2}&\frac{11}{2}\end{matrix}\right))$$

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

$$\frac{1408}{3}\times \frac{11}{2}-\frac{19}{3}\times \frac{1099}{2}$$

Multiply \frac{1408}{3} times \frac{11}{2} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$\frac{7744}{3}-\frac{19}{3}\times \frac{1099}{2}$$

Multiply \frac{19}{3} times \frac{1099}{2} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$\frac{7744}{3}-\frac{20881}{6}$$

Subtract \frac{20881}{6} from \frac{7744}{3} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$-\frac{5393}{6}$$

Factor

$$-\frac{5393}{6} = -898\frac{5}{6} = -898.8333333333334$$