{lll}{4}&{5}&{6}{1}&{9}&{7}{4}&{9}&{5} eching

$$\left( \begin{array} { l l l } { 4 } & { 5 } & { 6 } \\ { 1 } & { 9 } & { 7 } \\ { 4 } & { 9 } & { 5 } \end{array} \right)$$

Determinantni hisoblash

$$-119$$

Sarrus qoidasidan foydalanish qadamlari

Diagonal usulidan foydalanib matritsaning aniqlovchisini topish.

$$det(\left(\begin{matrix}4&5&6\\1&9&7\\4&9&5\end{matrix}\right))$$

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

$$\left(\begin{matrix}4&5&6&4&5\\1&9&7&1&9\\4&9&5&4&9\end{matrix}\right)$$

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

$$4\times 9\times 5+5\times 7\times 4+6\times 9=374$$

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

$$4\times 9\times 6+9\times 7\times 4+5\times 5=493$$

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

$$374-493$$

374 dan 493 ni ayirish.

$$-119$$

Ikkilamchilar bilan kengayishdan foydalanish qadamlari

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

$$det(\left(\begin{matrix}4&5&6\\1&9&7\\4&9&5\end{matrix}\right))$$

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.

$$4det(\left(\begin{matrix}9&7\\9&5\end{matrix}\right))-5det(\left(\begin{matrix}1&7\\4&5\end{matrix}\right))+6det(\left(\begin{matrix}1&9\\4&9\end{matrix}\right))$$

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

$$4\left(9\times 5-9\times 7\right)-5\left(5-4\times 7\right)+6\left(9-4\times 9\right)$$

Qisqartirish.

$$4\left(-18\right)-5\left(-23\right)+6\left(-27\right)$$

Yakuniy natija olish uchun shartlarni qo'shish.

$$-119$$

Baholash

$$\left(\begin{matrix}4&5&6\\1&9&7\\4&9&5\end{matrix}\right)$$