Issolvi {ccc}{3}&{-1}&{4}{2}&{3}&{-1}{-5}&{2}&{3}

Evalwa

Fattur

Kwizz

5 problemi simili għal:

Problemi Simili mit-Tiftix tal-Web

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-6-3-1-0-3-3-9-0-0

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-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}3&-1&4\\2&3&-1\\-5&2&3\end{matrix}\right))

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

\left(\begin{matrix}3&-1&4&3&-1\\2&3&-1&2&3\\-5&2&3&-5&2\end{matrix}\right)

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

3\times 3\times 3-\left(-\left(-5\right)\right)+4\times 2\times 2=38

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

-5\times 3\times 4+2\left(-1\right)\times 3+3\times 2\left(-1\right)=-72

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

38-\left(-72\right)

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

110

Naqqas -72 minn 38.

det(\left(\begin{matrix}3&-1&4\\2&3&-1\\-5&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).

3det(\left(\begin{matrix}3&-1\\2&3\end{matrix}\right))-\left(-det(\left(\begin{matrix}2&-1\\-5&3\end{matrix}\right))\right)+4det(\left(\begin{matrix}2&3\\-5&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.

3\left(3\times 3-2\left(-1\right)\right)-\left(-\left(2\times 3-\left(-5\left(-1\right)\right)\right)\right)+4\left(2\times 2-\left(-5\times 3\right)\right)

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

3\times 11-\left(-1\right)+4\times 19

Issimplifika.

110

Żid it-termini li tikseb ir-riżultat finali.