Issolvi {ccc}{265}&{240}&{219}{240}&{225}&{198}{219}&{198}&{181}

Evalwa

Fattur

Kwizz

Problemi Simili mit-Tiftix tal-Web

https://socratic.org/questions/the-value-of-determinant-a-b-c-2a-2a-2b-b-c-a-2b-2c-2c-c-a-b-is

https://www.quora.com/Evaluate-the-following-determinant-If-S_n-alpha-n+-beta-n+-gamma-n-then-what-is-the-value-of-left-begin-array-ccc-S_0-S_1-S_2-S_1-S_2-S_3-S_2-S_3-S_4-end-array-right

https://socratic.org/questions/how-do-you-find-the-determinant-of-1-5-3-6-2-3-4-3-0-5-2-2-1-6-8-2-6-6

https://math.stackexchange.com/questions/191148/what-is-the-largest-determinant-you-can-get-by-filling-in-0-1-or-2-into-a-4-by-4

Sehem

Ikkupjat fuq il-klibbord

det(\left(\begin{matrix}265&240&219\\240&225&198\\219&198&181\end{matrix}\right))

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

\left(\begin{matrix}265&240&219&265&240\\240&225&198&240&225\\219&198&181&219&198\end{matrix}\right)

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

265\times 225\times 181+240\times 198\times 219+219\times 240\times 198=31605885

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

219\times 225\times 219+198\times 198\times 265+181\times 240\times 240=31605885

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

31605885-31605885

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

Naqqas 31605885 minn 31605885.

det(\left(\begin{matrix}265&240&219\\240&225&198\\219&198&181\end{matrix}\right))

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

265det(\left(\begin{matrix}225&198\\198&181\end{matrix}\right))-240det(\left(\begin{matrix}240&198\\219&181\end{matrix}\right))+219det(\left(\begin{matrix}240&225\\219&198\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.

265\left(225\times 181-198\times 198\right)-240\left(240\times 181-219\times 198\right)+219\left(240\times 198-219\times 225\right)

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

265\times 1521-240\times 78+219\left(-1755\right)

Issimplifika.

Żid it-termini li tikseb ir-riżultat finali.