{lll}{11}&{21}&{31}{21}&{31}&{4}{31}&{41}&{51} eching

$$\left| \begin{array} { l l l } { 11 } & { 21 } & { 31 } \\ { 21 } & { 31 } & { 4 } \\ { 31 } & { 41 } & { 51 } \end{array} \right|$$

Baholash

$$-7400$$

Sarrus qoidasidan foydalanish qadamlari

Diagonal usulidan foydalanib matritsaning aniqlovchisini topish.

$$det(\left(\begin{matrix}11&21&31\\21&31&4\\31&41&51\end{matrix}\right))$$

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

$$\left(\begin{matrix}11&21&31&11&21\\21&31&4&21&31\\31&41&51&31&41\end{matrix}\right)$$

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

$$11\times 31\times 51+21\times 4\times 31+31\times 21\times 41=46686$$

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

$$31\times 31\times 31+41\times 4\times 11+51\times 21\times 21=54086$$

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

$$46686-54086$$

46686 dan 54086 ni ayirish.

$$-7400$$

Ikkilamchilar bilan kengayishdan foydalanish qadamlari

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

$$det(\left(\begin{matrix}11&21&31\\21&31&4\\31&41&51\end{matrix}\right))$$

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.

$$11det(\left(\begin{matrix}31&4\\41&51\end{matrix}\right))-21det(\left(\begin{matrix}21&4\\31&51\end{matrix}\right))+31det(\left(\begin{matrix}21&31\\31&41\end{matrix}\right))$$

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

$$11\left(31\times 51-41\times 4\right)-21\left(21\times 51-31\times 4\right)+31\left(21\times 41-31\times 31\right)$$

Qisqartirish.

$$11\times 1417-21\times 947+31\left(-100\right)$$

Yakuniy natija olish uchun shartlarni qo'shish.

$$-7400$$

Omil

$$-7400$$