{lll}{1}&{3}&{2}{4}&{1}&{3}{2}&{2}&{0} eching

$$\left( \begin{array} { l l l } { 1 } & { 3 } & { 2 } \\ { 4 } & { 1 } & { 3 } \\ { 2 } & { 2 } & { 0 } \end{array} \right)$$

Determinantni hisoblash

$$24$$

Sarrus qoidasidan foydalanish qadamlari

Diagonal usulidan foydalanib matritsaning aniqlovchisini topish.

$$det(\left(\begin{matrix}1&3&2\\4&1&3\\2&2&0\end{matrix}\right))$$

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

$$\left(\begin{matrix}1&3&2&1&3\\4&1&3&4&1\\2&2&0&2&2\end{matrix}\right)$$

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

$$3\times 3\times 2+2\times 4\times 2=34$$

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

$$2\times 2+2\times 3=10$$

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

$$34-10$$

34 dan 10 ni ayirish.

$$24$$

Ikkilamchilar bilan kengayishdan foydalanish qadamlari

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

$$det(\left(\begin{matrix}1&3&2\\4&1&3\\2&2&0\end{matrix}\right))$$

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.

$$det(\left(\begin{matrix}1&3\\2&0\end{matrix}\right))-3det(\left(\begin{matrix}4&3\\2&0\end{matrix}\right))+2det(\left(\begin{matrix}4&1\\2&2\end{matrix}\right))$$

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

$$-2\times 3-3\left(-2\times 3\right)+2\left(4\times 2-2\right)$$

Qisqartirish.

$$-6-3\left(-6\right)+2\times 6$$

Yakuniy natija olish uchun shartlarni qo'shish.

$$24$$

Baholash

$$\left(\begin{matrix}1&3&2\\4&1&3\\2&2&0\end{matrix}\right)$$