{rrr}{-1}&{-1}&{1}{0}&{0}&{-1}{1}&{1}&{1} eching

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

Determinantni hisoblash

$$0$$

Sarrus qoidasidan foydalanish qadamlari

Diagonal usulidan foydalanib matritsaning aniqlovchisini topish.

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

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

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

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

$$-\left(-1\right)=1$$

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

$$1-1$$

1 dan 1 ni ayirish.

$$0$$

Ikkilamchilar bilan kengayishdan foydalanish qadamlari

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

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

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.

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

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

$$-\left(-\left(-1\right)\right)-\left(-\left(-\left(-1\right)\right)\right)$$

Qisqartirish.

$$-1-\left(-1\right)$$

Yakuniy natija olish uchun shartlarni qo'shish.

$$0$$

Baholash

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