Issolvi {ccc}{1}&{1}&{22}{5}&{-2}&{7}{2}&{-5}&{4}

Evalwa

Fattur

Kwizz

Problemi Simili mit-Tiftix tal-Web

https://socratic.org/questions/how-do-you-find-the-determinant-of-0-1-4-3-2-3-8-3-4

https://socratic.org/questions/how-do-you-find-the-determinant-of-2-1-3-3-0-2-1-3-0

https://socratic.org/questions/how-do-you-find-the-value-of-the-determinant-4-1-0-5-15-1-2-10-7

https://socratic.org/questions/how-do-you-find-the-determinant-of-8-9-3-3-5-7-1-2-4

https://socratic.org/questions/how-do-you-find-the-determinant-of-4-6-7-3-2-4-1-1-1

Sehem

Ikkupjat fuq il-klibbord

det(\left(\begin{matrix}1&1&22\\5&-2&7\\2&-5&4\end{matrix}\right))

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

\left(\begin{matrix}1&1&22&1&1\\5&-2&7&5&-2\\2&-5&4&2&-5\end{matrix}\right)

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

-2\times 4+7\times 2+22\times 5\left(-5\right)=-544

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

2\left(-2\right)\times 22-5\times 7+4\times 5=-103

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

-544-\left(-103\right)

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

-441

Naqqas -103 minn -544.

det(\left(\begin{matrix}1&1&22\\5&-2&7\\2&-5&4\end{matrix}\right))

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

det(\left(\begin{matrix}-2&7\\-5&4\end{matrix}\right))-det(\left(\begin{matrix}5&7\\2&4\end{matrix}\right))+22det(\left(\begin{matrix}5&-2\\2&-5\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.

-2\times 4-\left(-5\times 7\right)-\left(5\times 4-2\times 7\right)+22\left(5\left(-5\right)-2\left(-2\right)\right)

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

27-6+22\left(-21\right)

Issimplifika.

-441

Żid it-termini li tikseb ir-riżultat finali.