\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.
Kalkulahin ang Determinant
\frac{15619}{18000} = 0.8677222222222222
I-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)
Ibahagi
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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))
Idagdag ang \frac{1}{4} at \frac{1}{3} para makuha ang \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))
I-multiply ang \frac{7}{12} at 12 para makuha ang 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))
I-multiply ang \frac{12}{5} at \frac{7}{5} para makuha ang \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))
Idagdag ang \frac{84}{25} at \frac{3}{5} para makuha ang \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))
Idagdag ang \frac{2}{3} at \frac{1}{3} para makuha ang 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))
I-divide ang 1 gamit ang \frac{2}{3} sa pamamagitan ng pagmu-multiply sa 1 gamit ang reciprocal ng \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))
I-multiply ang 1 at \frac{3}{2} para makuha ang \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))
I-multiply ang 1 at 7 para makuha ang 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))
Idagdag ang 7 at 5 para makuha ang 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))
I-multiply ang 2 at 4 para makuha ang 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))
Idagdag ang 8 at 3 para makuha ang 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))
Idagdag ang \frac{12}{7} at \frac{11}{4} para makuha ang \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))
Idagdag ang \frac{125}{28} at \frac{2}{7} para makuha ang \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))
I-divide ang \frac{1}{\frac{5}{7}} gamit ang \frac{5}{7} sa pamamagitan ng pagmu-multiply sa \frac{1}{\frac{5}{7}} gamit ang reciprocal ng \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))
I-multiply ang \frac{5}{7} at 5 para makuha ang \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))
I-divide ang 7 gamit ang \frac{25}{7} sa pamamagitan ng pagmu-multiply sa 7 gamit ang reciprocal ng \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))
I-multiply ang 7 at \frac{7}{25} para makuha ang \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))
I-multiply ang \frac{1}{8} at \frac{2}{3} para makuha ang \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))
Idagdag ang \frac{1}{12} at \frac{1}{3} para makuha ang \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))
I-multiply ang \frac{3}{5} at \frac{1}{3} para makuha ang \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))
Idagdag ang \frac{1}{5} at \frac{1}{4} para makuha ang \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))
I-multiply ang 1 at 4 para makuha ang 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))
Idagdag ang 4 at 1 para makuha ang 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))
I-subtract ang 1 mula sa \frac{5}{4} para makuha ang \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))
I-multiply ang \frac{8}{3} at \frac{1}{4} para makuha ang \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))
I-cancel out ang \frac{7}{4} at \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)
Palawakin ang orihinal na matrix sa pamamagitan ng pag-uulit sa unang dalawang column bilang ang ikaapat at ikalimang column.
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}
Simula sa kaliwang entry sa itaas, mag-multiply pababa sa hilera ng mga diagonal, at idagdag ang mga magreresultang product.
\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}
Simula sa kaliwang entry sa ibaba, mag-multiply pataas sa hilera ng mga diagonal, at idagdag ang mga magreresultang product.
\frac{54907}{6000}-\frac{74551}{9000}
I-subtract ang sum ng mga upward diagonal product mula sa sum ng mga downward diagonal product.
\frac{15619}{18000}
I-subtract ang \frac{74551}{9000} mula sa \frac{54907}{6000} sa pamamagitan ng paghahanap ng common denominator at pagsu-subtract sa mga numerator. Pagkatapos, i-reduce ang fraction sa lowest terms nito kung posible.
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))
Idagdag ang \frac{1}{4} at \frac{1}{3} para makuha ang \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))
I-multiply ang \frac{7}{12} at 12 para makuha ang 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))
I-multiply ang \frac{12}{5} at \frac{7}{5} para makuha ang \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))
Idagdag ang \frac{84}{25} at \frac{3}{5} para makuha ang \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))
Idagdag ang \frac{2}{3} at \frac{1}{3} para makuha ang 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))
I-divide ang 1 gamit ang \frac{2}{3} sa pamamagitan ng pagmu-multiply sa 1 gamit ang reciprocal ng \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))
I-multiply ang 1 at \frac{3}{2} para makuha ang \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))
I-multiply ang 1 at 7 para makuha ang 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))
Idagdag ang 7 at 5 para makuha ang 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))
I-multiply ang 2 at 4 para makuha ang 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))
Idagdag ang 8 at 3 para makuha ang 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))
Idagdag ang \frac{12}{7} at \frac{11}{4} para makuha ang \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))
Idagdag ang \frac{125}{28} at \frac{2}{7} para makuha ang \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))
I-divide ang \frac{1}{\frac{5}{7}} gamit ang \frac{5}{7} sa pamamagitan ng pagmu-multiply sa \frac{1}{\frac{5}{7}} gamit ang reciprocal ng \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))
I-multiply ang \frac{5}{7} at 5 para makuha ang \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))
I-divide ang 7 gamit ang \frac{25}{7} sa pamamagitan ng pagmu-multiply sa 7 gamit ang reciprocal ng \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))
I-multiply ang 7 at \frac{7}{25} para makuha ang \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))
I-multiply ang \frac{1}{8} at \frac{2}{3} para makuha ang \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))
Idagdag ang \frac{1}{12} at \frac{1}{3} para makuha ang \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))
I-multiply ang \frac{3}{5} at \frac{1}{3} para makuha ang \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))
Idagdag ang \frac{1}{5} at \frac{1}{4} para makuha ang \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))
I-multiply ang 1 at 4 para makuha ang 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))
Idagdag ang 4 at 1 para makuha ang 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))
I-subtract ang 1 mula sa \frac{5}{4} para makuha ang \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))
I-multiply ang \frac{8}{3} at \frac{1}{4} para makuha ang \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))
I-cancel out ang \frac{7}{4} at \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))
Para i-expand gamit ang minors, i-multiply ang bawat element ng unang row gamit ang minor nito, na determinant ng 2\times 2 matrix na ginawa sa pamamagitan ng pagtatanggal sa row at column na naglalaman sa element na iyon, pagkatapos ay i-multiply gamit ang position sign ng element.
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)
Para sa 2\times 2 na matrix \left(\begin{matrix}a&b\\c&d\end{matrix}\right), ang determinant ay ad-bc.
7\times \frac{551}{2250}-\frac{99}{25}\times \frac{259}{240}+\frac{3}{2}\times \frac{3427}{1500}
Pasimplehin.
\frac{15619}{18000}
Idagdag ang mga term para makuha ang pinal na resulta.
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