Issolvi {lll}{18}&{-1}&{-1}{10}&{3}&{-2}{-2}&{-2}&{3}

Evalwa

Fattur

Kwizz

5 problemi simili għal:

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https://math.stackexchange.com/questions/2939089/taking-signs-out-of-columns-of-matrix

Sehem

Ikkupjat fuq il-klibbord

det(\left(\begin{matrix}18&-1&-1\\10&3&-2\\-2&-2&3\end{matrix}\right))

Sib id-determinanti tal-matriċi bl-użu tal-metodu tad-djagonali.

\left(\begin{matrix}18&-1&-1&18&-1\\10&3&-2&10&3\\-2&-2&3&-2&-2\end{matrix}\right)

Jestendi l-matriċi oriġinali billi jirrepeti l-ewwel żewġ kolonni bħala r-raba' u l-ħames kolonni.

18\times 3\times 3-\left(-2\left(-2\right)\right)-10\left(-2\right)=178

Ibda mill-entrata tax-xellug ta' fuq, immultiplika 'l isfel tul id-djagonali, u żid il-prodotti riżultanti.

-2\times 3\left(-1\right)-2\left(-2\right)\times 18+3\times 10\left(-1\right)=48

Ibda mill-entrata tax-xellug ta' taħt, immultiplika 'l fuq tul id-djagonali, u żid il-prodotti riżultanti.

178-48

Naqqas is-somma tal-prodotti dijagonali 'l fuq mis-somma tal-prodotti dijagonali 'l isfel.

130

Naqqas 48 minn 178.

det(\left(\begin{matrix}18&-1&-1\\10&3&-2\\-2&-2&3\end{matrix}\right))

Sib id-determinanti tal-matriċi bl-użu tal-metodu tal-espansjoni bil-minuri (magħrufa wkoll bħala l-espansjoni bil-kofatturi).

18det(\left(\begin{matrix}3&-2\\-2&3\end{matrix}\right))-\left(-det(\left(\begin{matrix}10&-2\\-2&3\end{matrix}\right))\right)-det(\left(\begin{matrix}10&3\\-2&-2\end{matrix}\right))

Biex tespandi minn minuri, immultiplika kull element tal-ewwel ringiela bil-minuri tiegħu, li huwa d-determinant tal-matriċi 2\times 2 maħluqa bit-tħassir tar-ringiela u l-kolonna li jkun fih dak l-element, imbagħad immultiplika b'dan is-sinjal tal-pożizzjoni tal-element.

18\left(3\times 3-\left(-2\left(-2\right)\right)\right)-\left(-\left(10\times 3-\left(-2\left(-2\right)\right)\right)\right)-\left(10\left(-2\right)-\left(-2\times 3\right)\right)

Għall-matriċi 2\times 2 \left(\begin{matrix}a&b\\c&d\end{matrix}\right), id-determinant huwa ad-bc.

18\times 5-\left(-26\right)-\left(-14\right)

Issimplifika.

130

Żid it-termini li tikseb ir-riżultat finali.