Issolvi {ccc}{6}&{-2}&{9}{-2}&{3}&{-1}{9}&{-1}&{3}

Evalwa

Fattur

Kwizz

5 problemi simili għal:

Problemi Simili mit-Tiftix tal-Web

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-2-1-3-3-0-2-1-3-0

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

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

Sehem

Ikkupjat fuq il-klibbord

det(\left(\begin{matrix}6&-2&9\\-2&3&-1\\9&-1&3\end{matrix}\right))

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

\left(\begin{matrix}6&-2&9&6&-2\\-2&3&-1&-2&3\\9&-1&3&9&-1\end{matrix}\right)

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

6\times 3\times 3-2\left(-1\right)\times 9+9\left(-2\right)\left(-1\right)=90

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

9\times 3\times 9-\left(-6\right)+3\left(-2\right)\left(-2\right)=261

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

90-261

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

-171

Naqqas 261 minn 90.

det(\left(\begin{matrix}6&-2&9\\-2&3&-1\\9&-1&3\end{matrix}\right))

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

6det(\left(\begin{matrix}3&-1\\-1&3\end{matrix}\right))-\left(-2det(\left(\begin{matrix}-2&-1\\9&3\end{matrix}\right))\right)+9det(\left(\begin{matrix}-2&3\\9&-1\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.

6\left(3\times 3-\left(-\left(-1\right)\right)\right)-\left(-2\left(-2\times 3-9\left(-1\right)\right)\right)+9\left(-2\left(-1\right)-9\times 3\right)

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

6\times 8-\left(-2\times 3\right)+9\left(-25\right)

Issimplifika.

-171

Żid it-termini li tikseb ir-riżultat finali.