{lll}{1}&{2}&{3}{4}&{5}&{6}{7}&{4}&{9} eching

$$\left| \begin{array} { l l l } { 1 } & { 2 } & { 3 } \\ { 4 } & { 5 } & { 6 } \\ { 7 } & { 4 } & { 9 } \end{array} \right|$$

Baholash

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Sarrus qoidasidan foydalanish qadamlari

Diagonal usulidan foydalanib matritsaning aniqlovchisini topish.

$$det(\left(\begin{matrix}1&2&3\\4&5&6\\7&4&9\end{matrix}\right))$$

Birinchi ikki ustunni to'rtinchi va beshinchi ustun sifatida qaytarish uchun asl matritsani kengaytirish.

$$\left(\begin{matrix}1&2&3&1&2\\4&5&6&4&5\\7&4&9&7&4\end{matrix}\right)$$

Pastki chap kiritmadan boshlab diagonal kamayish tarafga ko'paytirish ha koʻpaytmalarni qo'shish.

$$5\times 9+2\times 6\times 7+3\times 4\times 4=177$$

Pastki chap kiritmadan boshlab diagonal ko'payish tarafga koʻpaytirish va koʻpaytmalarni qoʻshish.

$$7\times 5\times 3+4\times 6+9\times 4\times 2=201$$

Kamayib boruvchi diagonal koʻpaytmalarning yig'indisidan ko'payib boruvchi diagonal koʻpaytmalar yig'indisini ayirish.

$$177-201$$

177 dan 201 ni ayirish.

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Ikkilamchilar bilan kengayishdan foydalanish qadamlari

Kichik a'zolarni kengaytirish usulidan foydalanib matritsaning aniqlovchisini topish (ko'paytiruvchilarni kengaytirish deb ham nomlanadi).

$$det(\left(\begin{matrix}1&2&3\\4&5&6\\7&4&9\end{matrix}\right))$$

Kichik a’zolarga kengaytirish uchun birinchi satrning har bir elementini o‘zining kichik a’zosiga ko‘paytiring, qaysiki ana shu elementga ega bo‘lgan satr va ustunni yo‘q qilish orqali yaratilgan 2\times 2 matritsasining maxraji hisoblanadi, so‘ngra elementning joylashuv belgisiga ko‘paytiring.

$$det(\left(\begin{matrix}5&6\\4&9\end{matrix}\right))-2det(\left(\begin{matrix}4&6\\7&9\end{matrix}\right))+3det(\left(\begin{matrix}4&5\\7&4\end{matrix}\right))$$

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

$$5\times 9-4\times 6-2\left(4\times 9-7\times 6\right)+3\left(4\times 4-7\times 5\right)$$

Qisqartirish.

$$21-2\left(-6\right)+3\left(-19\right)$$

Yakuniy natija olish uchun shartlarni qo'shish.

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Omil

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