{lll}{(1/4+1/3)*12}&{12/5*7/5+frac{3}{5}}&{(frac{2}{3}+frac{1}{3})divfrac{2}{3}}{1frac{5}{7}+2frac{3}{4}+frac{2}{7}}&{1divfrac{5}{7}divfrac{5}{7}}&{frac{1}{8}*frac{2}{3}+frac{1}{3}}{frac{3}{5}*frac{1}{3}+frac{1}{4}}&{frac{8}{3}*(1frac{1}{4}-1)}&{frac{7}{4}*frac{4}{15}divfrac{7}{4}}hline хәл итегез

$$\left. \begin{array} { l l l } { ( \frac { 1 } { 4 } + \frac { 1 } { 3 } ) \times 12 } & { \frac { 12 } { 5 } \times \frac { 7 } { 5 } + \frac { 3 } { 5 } } & { ( \frac { 2 } { 3 } + \frac { 1 } { 3 } ) \div \frac { 2 } { 3 } } \\ { 1 \frac { 5 } { 7 } + 2 \frac { 3 } { 4 } + \frac { 2 } { 7 } } & { 1 \div \frac { 5 } { 7 } \div \frac { 5 } { 7 } } & { \frac { 1 } { 8 } \times \frac { 2 } { 3 } + \frac { 1 } { 3 } } \\ { \frac { 3 } { 5 } \times \frac { 1 } { 3 } + \frac { 1 } { 4 } } & { \frac { 8 } { 3 } \times ( 1 \frac { 1 } { 4 } - 1 ) } & { \frac { 7 } { 4 } \times \frac { 4 } { 15 } \div \frac { 7 } { 4 } } \\ \hline \end{array} \right.$$

Җилгеләгечне исәпләгез

$$\frac{15619}{18000} = 0.8677222222222222$$

Sarrus кагыйдәсен куллану адымнары

\frac{7}{12} алу өчен, \frac{1}{4} һәм \frac{1}{3} өстәгез.

$$det(\left(\begin{matrix}\frac{7}{12}\times 12&\frac{12}{5}\times \frac{7}{5}+\frac{3}{5}&\frac{\frac{2}{3}+\frac{1}{3}}{\frac{2}{3}}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

7 алу өчен, \frac{7}{12} һәм 12 тапкырлагыз.

$$det(\left(\begin{matrix}7&\frac{12}{5}\times \frac{7}{5}+\frac{3}{5}&\frac{\frac{2}{3}+\frac{1}{3}}{\frac{2}{3}}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{84}{25} алу өчен, \frac{12}{5} һәм \frac{7}{5} тапкырлагыз.

$$det(\left(\begin{matrix}7&\frac{84}{25}+\frac{3}{5}&\frac{\frac{2}{3}+\frac{1}{3}}{\frac{2}{3}}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{99}{25} алу өчен, \frac{84}{25} һәм \frac{3}{5} өстәгез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{\frac{2}{3}+\frac{1}{3}}{\frac{2}{3}}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

1 алу өчен, \frac{2}{3} һәм \frac{1}{3} өстәгез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{1}{\frac{2}{3}}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

1'ны \frac{2}{3}'ның кире зурлыгына тапкырлап, 1'ны \frac{2}{3}'га бүлегез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&1\times \frac{3}{2}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{3}{2} алу өчен, 1 һәм \frac{3}{2} тапкырлагыз.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

7 алу өчен, 1 һәм 7 тапкырлагыз.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

12 алу өчен, 7 һәм 5 өстәгез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{12}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

8 алу өчен, 2 һәм 4 тапкырлагыз.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{12}{7}+\frac{8+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

11 алу өчен, 8 һәм 3 өстәгез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{12}{7}+\frac{11}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{125}{28} алу өчен, \frac{12}{7} һәм \frac{11}{4} өстәгез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{125}{28}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{19}{4} алу өчен, \frac{125}{28} һәм \frac{2}{7} өстәгез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{1}{\frac{5}{7}}'ны \frac{5}{7}'ның кире зурлыгына тапкырлап, \frac{1}{\frac{5}{7}}'ны \frac{5}{7}'га бүлегез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{7}{\frac{5}{7}\times 5}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{25}{7} алу өчен, \frac{5}{7} һәм 5 тапкырлагыз.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{7}{\frac{25}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

7'ны \frac{25}{7}'ның кире зурлыгына тапкырлап, 7'ны \frac{25}{7}'га бүлегез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&7\times \frac{7}{25}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{49}{25} алу өчен, 7 һәм \frac{7}{25} тапкырлагыз.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{1}{12} алу өчен, \frac{1}{8} һәм \frac{2}{3} тапкырлагыз.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{1}{12}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{5}{12} алу өчен, \frac{1}{12} һәм \frac{1}{3} өстәгез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{1}{5} алу өчен, \frac{3}{5} һәм \frac{1}{3} тапкырлагыз.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{1}{5}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{9}{20} алу өчен, \frac{1}{5} һәм \frac{1}{4} өстәгез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

4 алу өчен, 1 һәм 4 тапкырлагыз.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{8}{3}\left(\frac{4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

5 алу өчен, 4 һәм 1 өстәгез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{8}{3}\left(\frac{5}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{1}{4} алу өчен, \frac{5}{4} 1'нан алыгыз.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{8}{3}\times \frac{1}{4}&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{2}{3} алу өчен, \frac{8}{3} һәм \frac{1}{4} тапкырлагыз.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{2}{3}&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{7}{4} һәм \frac{7}{4} кыскарту.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{2}{3}&\frac{4}{15}\end{matrix}\right))$$

Беренче ике багананы дүртенче һәм бишенче баганалар буларак кабатлап, башлангыч матрицаны киңәйтегез.

$$\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}&7&\frac{99}{25}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}&\frac{19}{4}&\frac{49}{25}\\\frac{9}{20}&\frac{2}{3}&\frac{4}{15}&\frac{9}{20}&\frac{2}{3}\end{matrix}\right)$$

Өске сул язмасыннан башлап, диагональ буенча аска тапкырлагыз һәм нәтиҗә чыгарылмаларны өстәгез.

$$7\times \frac{49}{25}\times \frac{4}{15}+\frac{99}{25}\times \frac{5}{12}\times \frac{9}{20}+\frac{3}{2}\times \frac{19}{4}\times \frac{2}{3}=\frac{54907}{6000}$$

Астагы сул язмадан башлап, диагональ буенча өскә тапкырлагыз һәм нәтиҗә чыгарылмаларны өстәгез.

$$\frac{9}{20}\times \frac{49}{25}\times \frac{3}{2}+\frac{2}{3}\times \frac{5}{12}\times 7+\frac{4}{15}\times \frac{19}{4}\times \frac{99}{25}=\frac{74551}{9000}$$

Аскы диагональ чыгарылмалары суммасыннан өске диагональ чыгарылмалары суммасын алыгыз.

$$\frac{54907}{6000}-\frac{74551}{9000}$$

Гомуми ваклаучыны табып һәм санаучыларны алып, \frac{74551}{9000}'на \frac{54907}{6000}'нан алыгыз. Аннары вакланманы мөмкин булган иң түбән элементка кадәр киметегез.

$$\frac{15619}{18000}$$

Берәмлекләргә киңәйтүне куллану адымнары

\frac{7}{12} алу өчен, \frac{1}{4} һәм \frac{1}{3} өстәгез.

$$det(\left(\begin{matrix}\frac{7}{12}\times 12&\frac{12}{5}\times \frac{7}{5}+\frac{3}{5}&\frac{\frac{2}{3}+\frac{1}{3}}{\frac{2}{3}}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

7 алу өчен, \frac{7}{12} һәм 12 тапкырлагыз.

$$det(\left(\begin{matrix}7&\frac{12}{5}\times \frac{7}{5}+\frac{3}{5}&\frac{\frac{2}{3}+\frac{1}{3}}{\frac{2}{3}}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{84}{25} алу өчен, \frac{12}{5} һәм \frac{7}{5} тапкырлагыз.

$$det(\left(\begin{matrix}7&\frac{84}{25}+\frac{3}{5}&\frac{\frac{2}{3}+\frac{1}{3}}{\frac{2}{3}}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{99}{25} алу өчен, \frac{84}{25} һәм \frac{3}{5} өстәгез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{\frac{2}{3}+\frac{1}{3}}{\frac{2}{3}}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

1 алу өчен, \frac{2}{3} һәм \frac{1}{3} өстәгез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{1}{\frac{2}{3}}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

1'ны \frac{2}{3}'ның кире зурлыгына тапкырлап, 1'ны \frac{2}{3}'га бүлегез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&1\times \frac{3}{2}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{3}{2} алу өчен, 1 һәм \frac{3}{2} тапкырлагыз.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{1\times 7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

7 алу өчен, 1 һәм 7 тапкырлагыз.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{7+5}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

12 алу өчен, 7 һәм 5 өстәгез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{12}{7}+\frac{2\times 4+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

8 алу өчен, 2 һәм 4 тапкырлагыз.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{12}{7}+\frac{8+3}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

11 алу өчен, 8 һәм 3 өстәгез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{12}{7}+\frac{11}{4}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{125}{28} алу өчен, \frac{12}{7} һәм \frac{11}{4} өстәгез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{125}{28}+\frac{2}{7}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{19}{4} алу өчен, \frac{125}{28} һәм \frac{2}{7} өстәгез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{\frac{1}{\frac{5}{7}}}{\frac{5}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{1}{\frac{5}{7}}'ны \frac{5}{7}'ның кире зурлыгына тапкырлап, \frac{1}{\frac{5}{7}}'ны \frac{5}{7}'га бүлегез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{7}{\frac{5}{7}\times 5}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{25}{7} алу өчен, \frac{5}{7} һәм 5 тапкырлагыз.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{7}{\frac{25}{7}}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

7'ны \frac{25}{7}'ның кире зурлыгына тапкырлап, 7'ны \frac{25}{7}'га бүлегез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&7\times \frac{7}{25}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{49}{25} алу өчен, 7 һәм \frac{7}{25} тапкырлагыз.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{1}{8}\times \frac{2}{3}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{1}{12} алу өчен, \frac{1}{8} һәм \frac{2}{3} тапкырлагыз.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{1}{12}+\frac{1}{3}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{5}{12} алу өчен, \frac{1}{12} һәм \frac{1}{3} өстәгез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{3}{5}\times \frac{1}{3}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{1}{5} алу өчен, \frac{3}{5} һәм \frac{1}{3} тапкырлагыз.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{1}{5}+\frac{1}{4}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{9}{20} алу өчен, \frac{1}{5} һәм \frac{1}{4} өстәгез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{8}{3}\left(\frac{1\times 4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

4 алу өчен, 1 һәм 4 тапкырлагыз.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{8}{3}\left(\frac{4+1}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

5 алу өчен, 4 һәм 1 өстәгез.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{8}{3}\left(\frac{5}{4}-1\right)&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{1}{4} алу өчен, \frac{5}{4} 1'нан алыгыз.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{8}{3}\times \frac{1}{4}&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{2}{3} алу өчен, \frac{8}{3} һәм \frac{1}{4} тапкырлагыз.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{2}{3}&\frac{\frac{7}{4}\times \frac{4}{15}}{\frac{7}{4}}\end{matrix}\right))$$

\frac{7}{4} һәм \frac{7}{4} кыскарту.

$$det(\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{2}{3}&\frac{4}{15}\end{matrix}\right))$$

Берәмлекләргә киңәйтү өчен, беренче юлның һәр элементын элементны үз эченә алган юлны һәм багананы бетереп төзегән 2\times 2 матрицаның вакланмасы булган аның берәмлегенә тапкырлагыз, аннары элементның позициясе тамгасына тапкырлагыз.

$$7det(\left(\begin{matrix}\frac{49}{25}&\frac{5}{12}\\\frac{2}{3}&\frac{4}{15}\end{matrix}\right))-\frac{99}{25}det(\left(\begin{matrix}\frac{19}{4}&\frac{5}{12}\\\frac{9}{20}&\frac{4}{15}\end{matrix}\right))+\frac{3}{2}det(\left(\begin{matrix}\frac{19}{4}&\frac{49}{25}\\\frac{9}{20}&\frac{2}{3}\end{matrix}\right))$$

2\times 2 \left(\begin{matrix}a&b\\c&d\end{matrix}\right) матрицасы өчен детерминант - ad-bc.

$$7\left(\frac{49}{25}\times \frac{4}{15}-\frac{2}{3}\times \frac{5}{12}\right)-\frac{99}{25}\left(\frac{19}{4}\times \frac{4}{15}-\frac{9}{20}\times \frac{5}{12}\right)+\frac{3}{2}\left(\frac{19}{4}\times \frac{2}{3}-\frac{9}{20}\times \frac{49}{25}\right)$$

Гадиләштерегез.

$$7\times \frac{551}{2250}-\frac{99}{25}\times \frac{259}{240}+\frac{3}{2}\times \frac{3427}{1500}$$

Ахыргы нәтиҗәне алу өчен, элементларны өстәгез.

$$\frac{15619}{18000}$$

Исәпләгез

$$\left(\begin{matrix}7&\frac{99}{25}&\frac{3}{2}\\\frac{19}{4}&\frac{49}{25}&\frac{5}{12}\\\frac{9}{20}&\frac{2}{3}&\frac{4}{15}\end{matrix}\right)$$