{rrr}{1}&{-2}&{0}{4}&{-2}&{-1}{-3}&{1}&{2} eching

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

Determinantni hisoblash

$$7$$

Sarrus qoidasidan foydalanish qadamlari

Diagonal usulidan foydalanib matritsaning aniqlovchisini topish.

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

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

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

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

$$-2\times 2-2\left(-1\right)\left(-3\right)=-10$$

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

$$-1+2\times 4\left(-2\right)=-17$$

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

$$-10-\left(-17\right)$$

-10 dan -17 ni ayirish.

$$7$$

Ikkilamchilar bilan kengayishdan foydalanish qadamlari

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

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

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.

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

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

$$-2\times 2-\left(-1\right)-\left(-2\left(4\times 2-\left(-3\left(-1\right)\right)\right)\right)$$

Qisqartirish.

$$-3-\left(-2\times 5\right)$$

Yakuniy natija olish uchun shartlarni qo'shish.

$$7$$

Baholash

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