Solve {l|l}hline2/7+3/7-2/9&{1-(1/12+frac{5}{12})}hlinefrac{5}{9}-(frac{3}{5}-frac{4}{9})&{frac{1}{2}+frac{2}{5}+frac{1}{3}}hline

$$\left. \begin{array} { l | l } \hline \frac { 2 } { 7 } + \frac { 3 } { 7 } - \frac { 2 } { 9 } & { 1 - ( \frac { 1 } { 12 } + \frac { 5 } { 12 } ) } \\ \hline \frac { 5 } { 9 } - ( \frac { 3 } { 5 } - \frac { 4 } { 9 } ) & { \frac { 1 } { 2 } + \frac { 2 } { 5 } + \frac { 1 } { 3 } } \\ \hline \end{array} \right.$$

Calculate Determinant

$$\frac{769}{1890} = 0.4068783068783069$$

Steps Using Diagonal Rule

Add \frac{2}{7} and \frac{3}{7} to get \frac{5}{7}.

$$det(\left(\begin{matrix}\frac{5}{7}-\frac{2}{9}&1-\left(\frac{1}{12}+\frac{5}{12}\right)\\\frac{5}{9}-\left(\frac{3}{5}-\frac{4}{9}\right)&\frac{1}{2}+\frac{2}{5}+\frac{1}{3}\end{matrix}\right))$$

Subtract \frac{2}{9} from \frac{5}{7} to get \frac{31}{63}.

$$det(\left(\begin{matrix}\frac{31}{63}&1-\left(\frac{1}{12}+\frac{5}{12}\right)\\\frac{5}{9}-\left(\frac{3}{5}-\frac{4}{9}\right)&\frac{1}{2}+\frac{2}{5}+\frac{1}{3}\end{matrix}\right))$$

Add \frac{1}{12} and \frac{5}{12} to get \frac{1}{2}.

$$det(\left(\begin{matrix}\frac{31}{63}&1-\frac{1}{2}\\\frac{5}{9}-\left(\frac{3}{5}-\frac{4}{9}\right)&\frac{1}{2}+\frac{2}{5}+\frac{1}{3}\end{matrix}\right))$$

Subtract \frac{1}{2} from 1 to get \frac{1}{2}.

$$det(\left(\begin{matrix}\frac{31}{63}&\frac{1}{2}\\\frac{5}{9}-\left(\frac{3}{5}-\frac{4}{9}\right)&\frac{1}{2}+\frac{2}{5}+\frac{1}{3}\end{matrix}\right))$$

Subtract \frac{4}{9} from \frac{3}{5} to get \frac{7}{45}.

$$det(\left(\begin{matrix}\frac{31}{63}&\frac{1}{2}\\\frac{5}{9}-\frac{7}{45}&\frac{1}{2}+\frac{2}{5}+\frac{1}{3}\end{matrix}\right))$$

Subtract \frac{7}{45} from \frac{5}{9} to get \frac{2}{5}.

$$det(\left(\begin{matrix}\frac{31}{63}&\frac{1}{2}\\\frac{2}{5}&\frac{1}{2}+\frac{2}{5}+\frac{1}{3}\end{matrix}\right))$$

Add \frac{1}{2} and \frac{2}{5} to get \frac{9}{10}.

$$det(\left(\begin{matrix}\frac{31}{63}&\frac{1}{2}\\\frac{2}{5}&\frac{9}{10}+\frac{1}{3}\end{matrix}\right))$$

Add \frac{9}{10} and \frac{1}{3} to get \frac{37}{30}.

$$det(\left(\begin{matrix}\frac{31}{63}&\frac{1}{2}\\\frac{2}{5}&\frac{37}{30}\end{matrix}\right))$$

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

$$\frac{31}{63}\times \frac{37}{30}-\frac{1}{2}\times \frac{2}{5}$$

Multiply \frac{31}{63} times \frac{37}{30} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$\frac{1147}{1890}-\frac{1}{2}\times \frac{2}{5}$$

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

$$\frac{1147}{1890}-\frac{1}{5}$$

Subtract \frac{1}{5} from \frac{1147}{1890} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$\frac{769}{1890}$$

Evaluate

$$\left(\begin{matrix}\frac{31}{63}&\frac{1}{2}\\\frac{2}{5}&\frac{37}{30}\end{matrix}\right)$$