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det(\left(\begin{matrix}18&-1&-1\\10&3&-2\\-22&-2&3\end{matrix}\right))
Diagonal usulidan foydalanib matritsaning aniqlovchisini topish.
\left(\begin{matrix}18&-1&-1&18&-1\\10&3&-2&10&3\\-22&-2&3&-22&-2\end{matrix}\right)
Birinchi ikki ustunni to'rtinchi va beshinchi ustun sifatida qaytarish uchun asl matritsani kengaytirish.
18\times 3\times 3-\left(-2\left(-22\right)\right)-10\left(-2\right)=138
Pastki chap kiritmadan boshlab diagonal kamayish tarafga ko'paytirish ha koʻpaytmalarni qo'shish.
-22\times 3\left(-1\right)-2\left(-2\right)\times 18+3\times 10\left(-1\right)=108
Pastki chap kiritmadan boshlab diagonal ko'payish tarafga koʻpaytirish va koʻpaytmalarni qoʻshish.
138-108
Kamayib boruvchi diagonal koʻpaytmalarning yig'indisidan ko'payib boruvchi diagonal koʻpaytmalar yig'indisini ayirish.
30
138 dan 108 ni ayirish.
det(\left(\begin{matrix}18&-1&-1\\10&3&-2\\-22&-2&3\end{matrix}\right))
Kichik a'zolarni kengaytirish usulidan foydalanib matritsaning aniqlovchisini topish (ko'paytiruvchilarni kengaytirish deb ham nomlanadi).
18det(\left(\begin{matrix}3&-2\\-2&3\end{matrix}\right))-\left(-det(\left(\begin{matrix}10&-2\\-22&3\end{matrix}\right))\right)-det(\left(\begin{matrix}10&3\\-22&-2\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.
18\left(3\times 3-\left(-2\left(-2\right)\right)\right)-\left(-\left(10\times 3-\left(-22\left(-2\right)\right)\right)\right)-\left(10\left(-2\right)-\left(-22\times 3\right)\right)
2\times 2 matritsasi uchun \left(\begin{matrix}a&b\\c&d\end{matrix}\right), maxraj ad-bc.
18\times 5-\left(-\left(-14\right)\right)-46
Qisqartirish.
30
Yakuniy natija olish uchun shartlarni qo'shish.