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

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

Determinantni hisoblash

$$-7$$

Sarrus qoidasidan foydalanish qadamlari

Diagonal usulidan foydalanib matritsaning aniqlovchisini topish.

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

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

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

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

$$-4-3\left(-2\right)\times 3=14$$

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

$$-3+3\times 4\times 2=21$$

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

$$14-21$$

14 dan 21 ni ayirish.

$$-7$$

Ikkilamchilar bilan kengayishdan foydalanish qadamlari

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

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

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.

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

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

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

Qisqartirish.

$$2\left(-12\right)-\left(-\left(-4\right)\right)-3\left(-7\right)$$

Yakuniy natija olish uchun shartlarni qo'shish.

$$-7$$

Baholash

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