Issolvi {ccc}{1}&{-16}&{19}{7}&{-6}&{13}{3}&{6}&{4}

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-4-1-0-5-15-1-2-10-7

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-determinant-of-2-1-3-3-0-2-1-3-0

https://socratic.org/questions/how-to-calculate-this-abs-4-4-m-6-m-3-m-3-3-4

https://socratic.org/questions/how-do-you-find-the-value-of-the-determinant-6-3-1-0-3-3-9-0-0

Sehem

Ikkupjat fuq il-klibbord

det(\left(\begin{matrix}1&-16&19\\7&-6&13\\3&6&4\end{matrix}\right))

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

\left(\begin{matrix}1&-16&19&1&-16\\7&-6&13&7&-6\\3&6&4&3&6\end{matrix}\right)

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

-6\times 4-16\times 13\times 3+19\times 7\times 6=150

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

3\left(-6\right)\times 19+6\times 13+4\times 7\left(-16\right)=-712

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

150-\left(-712\right)

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

862

Naqqas -712 minn 150.

det(\left(\begin{matrix}1&-16&19\\7&-6&13\\3&6&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}-6&13\\6&4\end{matrix}\right))-\left(-16det(\left(\begin{matrix}7&13\\3&4\end{matrix}\right))\right)+19det(\left(\begin{matrix}7&-6\\3&6\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\times 4-6\times 13-\left(-16\left(7\times 4-3\times 13\right)\right)+19\left(7\times 6-3\left(-6\right)\right)

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

-102-\left(-16\left(-11\right)\right)+19\times 60

Issimplifika.

862

Żid it-termini li tikseb ir-riżultat finali.