\left. \begin{array} { l l l } { ( \frac { 1 } { 4 } + \frac { 1 } { 3 } ) \times 12 } & { \frac { 12 } { 5 } \times \frac { 7 } { 5 } + \frac { 3 } { 5 } } & { ( \frac { 2 } { 3 } + \frac { 1 } { 3 } ) \div \frac { 2 } { 3 } } \\ { 1 \frac { 5 } { 7 } + 2 \frac { 3 } { 4 } + \frac { 2 } { 7 } } & { 1 \div \frac { 5 } { 7 } \div \frac { 5 } { 7 } } & { \frac { 1 } { 8 } \times \frac { 2 } { 3 } + \frac { 1 } { 3 } } \\ { \frac { 3 } { 5 } \times \frac { 1 } { 3 } + \frac { 1 } { 4 } } & { \frac { 8 } { 3 } \times ( 1 \frac { 1 } { 4 } - 1 ) } & { \frac { 7 } { 4 } \times \frac { 4 } { 15 } \div \frac { 7 } { 4 } } \\ \hline \end{array} \right.
Calculate Determinant
\frac{15619}{18000} = 0.8677222222222222
Evaluate
\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{2}{3}&\frac{4}{15}\end{matrix}\right)
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det(\left(\begin{matrix}\frac{7}{12}\times 12&\frac{12}{5}\times \frac{7}{5}+\frac{3}{5}&\frac{\frac{2}{3}+\frac{1}{3}}{\frac{2}{3}}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Add \frac{1}{4} and \frac{1}{3} to get \frac{7}{12}.
det(\left(\begin{matrix}7&\frac{12}{5}\times \frac{7}{5}+\frac{3}{5}&\frac{\frac{2}{3}+\frac{1}{3}}{\frac{2}{3}}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Multiply \frac{7}{12} and 12 to get 7.
det(\left(\begin{matrix}7&\frac{84}{25}+\frac{3}{5}&\frac{\frac{2}{3}+\frac{1}{3}}{\frac{2}{3}}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Multiply \frac{12}{5} and \frac{7}{5} to get \frac{84}{25}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{\frac{2}{3}+\frac{1}{3}}{\frac{2}{3}}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Add \frac{84}{25} and \frac{3}{5} to get \frac{99}{25}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{1}{\frac{2}{3}}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Add \frac{2}{3} and \frac{1}{3} to get 1.
det(\left(\begin{matrix}7&\frac{99}{25}&1\times \frac{3}{2}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Divide 1 by \frac{2}{3} by multiplying 1 by the reciprocal of \frac{2}{3}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Multiply 1 and \frac{3}{2} to get \frac{3}{2}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Multiply 1 and 7 to get 7.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{12}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Add 7 and 5 to get 12.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{12}{7}+\frac{8+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Multiply 2 and 4 to get 8.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{12}{7}+\frac{11}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Add 8 and 3 to get 11.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{125}{28}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Add \frac{12}{7} and \frac{11}{4} to get \frac{125}{28}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Add \frac{125}{28} and \frac{2}{7} to get \frac{19}{4}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{7}{\frac{5}{7}\times 5}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Divide \frac{1}{\frac{5}{7}} by \frac{5}{7} by multiplying \frac{1}{\frac{5}{7}} by the reciprocal of \frac{5}{7}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{7}{\frac{25}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Multiply \frac{5}{7} and 5 to get \frac{25}{7}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&7\times \frac{7}{25}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Divide 7 by \frac{25}{7} by multiplying 7 by the reciprocal of \frac{25}{7}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Multiply 7 and \frac{7}{25} to get \frac{49}{25}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{1}{12}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Multiply \frac{1}{8} and \frac{2}{3} to get \frac{1}{12}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Add \frac{1}{12} and \frac{1}{3} to get \frac{5}{12}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{1}{5}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Multiply \frac{3}{5} and \frac{1}{3} to get \frac{1}{5}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Add \frac{1}{5} and \frac{1}{4} to get \frac{9}{20}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{8}{3}\left(\frac{4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Multiply 1 and 4 to get 4.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{8}{3}\left(\frac{5}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Add 4 and 1 to get 5.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{8}{3}\times \frac{1}{4}&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Subtract 1 from \frac{5}{4} to get \frac{1}{4}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{2}{3}&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Multiply \frac{8}{3} and \frac{1}{4} to get \frac{2}{3}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{2}{3}&\frac{4}{15}\end{matrix}\right))
Cancel out \frac{7}{4} and \frac{7}{4}.
\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}&7&\frac{99}{25}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}&\frac{19}{4}&\frac{49}{25}\\\frac{9}{20}&\frac{2}{3}&\frac{4}{15}&\frac{9}{20}&\frac{2}{3}\end{matrix}\right)
Extend the original matrix by repeating the first two columns as the fourth and fifth columns.
7\times \frac{49}{25}\times \frac{4}{15}+\frac{99}{25}\times \frac{5}{12}\times \frac{9}{20}+\frac{3}{2}\times \frac{19}{4}\times \frac{2}{3}=\frac{54907}{6000}
Starting at the upper left entry, multiply down along the diagonals, and add the resulting products.
\frac{9}{20}\times \frac{49}{25}\times \frac{3}{2}+\frac{2}{3}\times \frac{5}{12}\times 7+\frac{4}{15}\times \frac{19}{4}\times \frac{99}{25}=\frac{74551}{9000}
Starting at the lower left entry, multiply up along the diagonals, and add the resulting products.
\frac{54907}{6000}-\frac{74551}{9000}
Subtract the sum of the upward diagonal products from the sum of the downward diagonal products.
\frac{15619}{18000}
Subtract \frac{74551}{9000} from \frac{54907}{6000} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.
det(\left(\begin{matrix}\frac{7}{12}\times 12&\frac{12}{5}\times \frac{7}{5}+\frac{3}{5}&\frac{\frac{2}{3}+\frac{1}{3}}{\frac{2}{3}}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Add \frac{1}{4} and \frac{1}{3} to get \frac{7}{12}.
det(\left(\begin{matrix}7&\frac{12}{5}\times \frac{7}{5}+\frac{3}{5}&\frac{\frac{2}{3}+\frac{1}{3}}{\frac{2}{3}}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Multiply \frac{7}{12} and 12 to get 7.
det(\left(\begin{matrix}7&\frac{84}{25}+\frac{3}{5}&\frac{\frac{2}{3}+\frac{1}{3}}{\frac{2}{3}}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Multiply \frac{12}{5} and \frac{7}{5} to get \frac{84}{25}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{\frac{2}{3}+\frac{1}{3}}{\frac{2}{3}}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Add \frac{84}{25} and \frac{3}{5} to get \frac{99}{25}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{1}{\frac{2}{3}}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Add \frac{2}{3} and \frac{1}{3} to get 1.
det(\left(\begin{matrix}7&\frac{99}{25}&1\times \frac{3}{2}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Divide 1 by \frac{2}{3} by multiplying 1 by the reciprocal of \frac{2}{3}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Multiply 1 and \frac{3}{2} to get \frac{3}{2}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Multiply 1 and 7 to get 7.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{12}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Add 7 and 5 to get 12.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{12}{7}+\frac{8+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Multiply 2 and 4 to get 8.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{12}{7}+\frac{11}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Add 8 and 3 to get 11.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{125}{28}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Add \frac{12}{7} and \frac{11}{4} to get \frac{125}{28}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Add \frac{125}{28} and \frac{2}{7} to get \frac{19}{4}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{7}{\frac{5}{7}\times 5}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Divide \frac{1}{\frac{5}{7}} by \frac{5}{7} by multiplying \frac{1}{\frac{5}{7}} by the reciprocal of \frac{5}{7}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{7}{\frac{25}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Multiply \frac{5}{7} and 5 to get \frac{25}{7}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&7\times \frac{7}{25}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Divide 7 by \frac{25}{7} by multiplying 7 by the reciprocal of \frac{25}{7}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Multiply 7 and \frac{7}{25} to get \frac{49}{25}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{1}{12}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Multiply \frac{1}{8} and \frac{2}{3} to get \frac{1}{12}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Add \frac{1}{12} and \frac{1}{3} to get \frac{5}{12}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{1}{5}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Multiply \frac{3}{5} and \frac{1}{3} to get \frac{1}{5}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Add \frac{1}{5} and \frac{1}{4} to get \frac{9}{20}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{8}{3}\left(\frac{4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Multiply 1 and 4 to get 4.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{8}{3}\left(\frac{5}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Add 4 and 1 to get 5.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{8}{3}\times \frac{1}{4}&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Subtract 1 from \frac{5}{4} to get \frac{1}{4}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{2}{3}&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))
Multiply \frac{8}{3} and \frac{1}{4} to get \frac{2}{3}.
det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{2}{3}&\frac{4}{15}\end{matrix}\right))
Cancel out \frac{7}{4} and \frac{7}{4}.
7det(\left(\begin{matrix}\frac{49}{25}&\frac{5}{12}\\\frac{2}{3}&\frac{4}{15}\end{matrix}\right))-\frac{99}{25}det(\left(\begin{matrix}\frac{19}{4}&\frac{5}{12}\\\frac{9}{20}&\frac{4}{15}\end{matrix}\right))+\frac{3}{2}det(\left(\begin{matrix}\frac{19}{4}&\frac{49}{25}\\\frac{9}{20}&\frac{2}{3}\end{matrix}\right))
To expand by minors, multiply each element of the first row by its minor, which is the determinant of the 2\times 2 matrix created by deleting the row and column containing that element, then multiply by the element's position sign.
7\left(\frac{49}{25}\times \frac{4}{15}-\frac{2}{3}\times \frac{5}{12}\right)-\frac{99}{25}\left(\frac{19}{4}\times \frac{4}{15}-\frac{9}{20}\times \frac{5}{12}\right)+\frac{3}{2}\left(\frac{19}{4}\times \frac{2}{3}-\frac{9}{20}\times \frac{49}{25}\right)
For the 2\times 2 matrix \left(\begin{matrix}a&b\\c&d\end{matrix}\right), the determinant is ad-bc.
7\times \frac{551}{2250}-\frac{99}{25}\times \frac{259}{240}+\frac{3}{2}\times \frac{3427}{1500}
Simplify.
\frac{15619}{18000}
Add the terms to obtain the final result.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}