{lll}{3}&{5}&{1}{x}&{0}&{1}{-4}&{-6}&{1} eching

$$\left| \begin{array} { l l l } { 3 } & { 5 } & { 1 } \\ { x } & { 0 } & { 1 } \\ { - 4 } & { - 6 } & { 1 } \end{array} \right|$$

Baholash

$$-11x-2$$

Sarrus qoidasidan foydalanish qadamlari

Diagonal usulidan foydalanib matritsaning aniqlovchisini topish.

$$det(\left(\begin{matrix}3&5&1\\x&0&1\\-4&-6&1\end{matrix}\right))$$

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

$$\left(\begin{matrix}3&5&1&3&5\\x&0&1&x&0\\-4&-6&1&-4&-6\end{matrix}\right)$$

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

$$5\left(-4\right)+x\left(-6\right)=-6x-20$$

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

$$-6\times 3+x\times 5=5x-18$$

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

$$-6x-20-\left(5x-18\right)$$

-20-6x dan -18+5x ni ayirish.

$$-11x-2$$

Ikkilamchilar bilan kengayishdan foydalanish qadamlari

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

$$det(\left(\begin{matrix}3&5&1\\x&0&1\\-4&-6&1\end{matrix}\right))$$

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.

$$3det(\left(\begin{matrix}0&1\\-6&1\end{matrix}\right))-5det(\left(\begin{matrix}x&1\\-4&1\end{matrix}\right))+det(\left(\begin{matrix}x&0\\-4&-6\end{matrix}\right))$$

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

$$3\left(-\left(-6\right)\right)-5\left(x-\left(-4\right)\right)+x\left(-6\right)$$

Qisqartirish.

$$3\times 6-5\left(x+4\right)-6x$$

Yakuniy natija olish uchun shartlarni qo'shish.

$$-11x-2$$

x'ga havola qilib birlashtirish

$$-\frac{11x^{2}}{2}-2x+С$$