{lll}{1}&{4}&{7}{2}&{5}&{8}{3}&{6}&{9} eching

$$\left( \begin{array} { l l l } { 1 } & { 4 } & { 7 } \\ { 2 } & { 5 } & { 8 } \\ { 3 } & { 6 } & { 9 } \end{array} \right)$$

Determinantni hisoblash

$$0$$

Sarrus qoidasidan foydalanish qadamlari

Diagonal usulidan foydalanib matritsaning aniqlovchisini topish.

$$det(\left(\begin{matrix}1&4&7\\2&5&8\\3&6&9\end{matrix}\right))$$

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

$$\left(\begin{matrix}1&4&7&1&4\\2&5&8&2&5\\3&6&9&3&6\end{matrix}\right)$$

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

$$5\times 9+4\times 8\times 3+7\times 2\times 6=225$$

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

$$3\times 5\times 7+6\times 8+9\times 2\times 4=225$$

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

$$225-225$$

225 dan 225 ni ayirish.

$$0$$

Ikkilamchilar bilan kengayishdan foydalanish qadamlari

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

$$det(\left(\begin{matrix}1&4&7\\2&5&8\\3&6&9\end{matrix}\right))$$

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.

$$det(\left(\begin{matrix}5&8\\6&9\end{matrix}\right))-4det(\left(\begin{matrix}2&8\\3&9\end{matrix}\right))+7det(\left(\begin{matrix}2&5\\3&6\end{matrix}\right))$$

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

$$5\times 9-6\times 8-4\left(2\times 9-3\times 8\right)+7\left(2\times 6-3\times 5\right)$$

Qisqartirish.

$$-3-4\left(-6\right)+7\left(-3\right)$$

Yakuniy natija olish uchun shartlarni qo'shish.

$$0$$

Baholash

$$\left(\begin{matrix}1&4&7\\2&5&8\\3&6&9\end{matrix}\right)$$