{ccc}{-7}&{-1}&{1}{-6}&{0}&{1/2}{-1}&{1}&{1} eching

$$\left| \begin{array} { c c c } { - 7 } & { - 1 } & { 1 } \\ { - 6 } & { 0 } & { \frac { 1 } { 2 } } \\ { - 1 } & { 1 } & { 1 } \end{array} \right|$$

Baholash

$$-8$$

Sarrus qoidasidan foydalanish qadamlari

Diagonal usulidan foydalanib matritsaning aniqlovchisini topish.

$$det(\left(\begin{matrix}-7&-1&1\\-6&0&\frac{1}{2}\\-1&1&1\end{matrix}\right))$$

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

$$\left(\begin{matrix}-7&-1&1&-7&-1\\-6&0&\frac{1}{2}&-6&0\\-1&1&1&-1&1\end{matrix}\right)$$

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

$$-\frac{1}{2}\left(-1\right)-6=-\frac{11}{2}$$

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

$$\frac{1}{2}\left(-7\right)-6\left(-1\right)=\frac{5}{2}$$

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

$$-\frac{11}{2}-\frac{5}{2}$$

Umumiy maxrajni topib va suratlarni ayirib \frac{5}{2} ni -\frac{11}{2} dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

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Ikkilamchilar bilan kengayishdan foydalanish qadamlari

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

$$det(\left(\begin{matrix}-7&-1&1\\-6&0&\frac{1}{2}\\-1&1&1\end{matrix}\right))$$

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.

$$-7det(\left(\begin{matrix}0&\frac{1}{2}\\1&1\end{matrix}\right))-\left(-det(\left(\begin{matrix}-6&\frac{1}{2}\\-1&1\end{matrix}\right))\right)+det(\left(\begin{matrix}-6&0\\-1&1\end{matrix}\right))$$

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

$$-7\left(-\frac{1}{2}\right)-\left(-\left(-6-\left(-\frac{1}{2}\right)\right)\right)-6$$

Qisqartirish.

$$-7\left(-\frac{1}{2}\right)-\left(-\left(-\frac{11}{2}\right)\right)-6$$

Yakuniy natija olish uchun shartlarni qo'shish.

$$-8$$

Omil

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