{lll}{5}&{4}&{1}{0}&{9}&{7}{8}&{1}&{0} eching

$$\left| \begin{array} { l l l } { 5 } & { 4 } & { 1 } \\ { 0 } & { 9 } & { 7 } \\ { 8 } & { 1 } & { 0 } \end{array} \right|$$

Baholash

$$117$$

Sarrus qoidasidan foydalanish qadamlari

Diagonal usulidan foydalanib matritsaning aniqlovchisini topish.

$$det(\left(\begin{matrix}5&4&1\\0&9&7\\8&1&0\end{matrix}\right))$$

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

$$\left(\begin{matrix}5&4&1&5&4\\0&9&7&0&9\\8&1&0&8&1\end{matrix}\right)$$

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

$$4\times 7\times 8=224$$

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

$$8\times 9+7\times 5=107$$

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

$$224-107$$

224 dan 107 ni ayirish.

$$117$$

Ikkilamchilar bilan kengayishdan foydalanish qadamlari

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

$$det(\left(\begin{matrix}5&4&1\\0&9&7\\8&1&0\end{matrix}\right))$$

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.

$$5det(\left(\begin{matrix}9&7\\1&0\end{matrix}\right))-4det(\left(\begin{matrix}0&7\\8&0\end{matrix}\right))+det(\left(\begin{matrix}0&9\\8&1\end{matrix}\right))$$

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

$$5\left(-7\right)-4\left(-8\times 7\right)-8\times 9$$

Qisqartirish.

$$5\left(-7\right)-4\left(-56\right)-72$$

Yakuniy natija olish uchun shartlarni qo'shish.

$$117$$

Omil

$$3^{2}\times 13$$