{ccc}{i}&{j}&{k}{1}&{-2}&{2}{3}&{2}&{0} eching

$$\left| \begin{array} { c c c } { i } & { j } & { k } \\ { 1 } & { - 2 } & { 2 } \\ { 3 } & { 2 } & { 0 } \end{array} \right|$$

Baholash

$$6j+8k-4i$$

Sarrus qoidasidan foydalanish qadamlari

Diagonal usulidan foydalanib matritsaning aniqlovchisini topish.

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

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

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

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

$$j\times 2\times 3+k\times 2=6j+2k$$

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

$$3\left(-2\right)k+2\times \left(2i\right)=4i-6k$$

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

$$6j+2k-\left(4i-6k\right)$$

6j+2k dan -6k+4i ni ayirish.

$$6j+8k-4i$$

Ikkilamchilar bilan kengayishdan foydalanish qadamlari

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

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

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.

$$idet(\left(\begin{matrix}-2&2\\2&0\end{matrix}\right))-jdet(\left(\begin{matrix}1&2\\3&0\end{matrix}\right))+kdet(\left(\begin{matrix}1&-2\\3&2\end{matrix}\right))$$

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

$$i\left(-2\times 2\right)-j\left(-3\times 2\right)+k\left(2-3\left(-2\right)\right)$$

Qisqartirish.

$$-4i-j\left(-6\right)+k\times 8$$

Yakuniy natija olish uchun shartlarni qo'shish.

$$6j+8k-4i$$