Whakaoti i te {ccc}{265}&{240}&{219}{240}&{225}&{198}{219}&{198}&{181}

Aromātai

Tauwehe

Pātaitai

Ngā Raru Ōrite mai i te Rapu Tukutuku

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

Tohaina

Kua tāruatia ki te papatopenga

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

Kimihia te tau whakatau o te poukapa mā te whakamahi i te tikanga hauroki.

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

Whakaroatia te poukapa taketake mā te tāruarua i ngā tīwae tuatahi e rua hei tīwae tuawhā me te tuarima.

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

Tīmata atu i te tāurunga mauī o runga, whakareatia whakararo i ngā hauroki, ka tāpiri i ngā hua ka puta.

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

Tīmata atu i te tāurunga mauī o raro, whakareatia whakarunga i ngā hauroki, ka tāpiri i ngā hua ka puta.

31605885-31605885

Tangohia te tapeke o ngā hauroki whakarunga mai i te tapeke o ngā hua hauroki whakararo.

Tango 31605885 mai i 31605885.

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

Kimihia te tau whakatau o te poukapa mā te whakamahi i te tikanga whakaroha ā-tauriki (te tikanga whakaroha ā-tauwehe tahi rānei).

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))

Hei whakaroha mā ngā tauriki, me whakarea ia huānga o te haupae tuatahi ki tana tauriki, arā, ko te tau whakatau o te poukapa 2\times 2 i hangā mā te muku i te haupae me te tīwae i roto anō taua huānga, kātahi ka whakarea ki te tohu tūnga o taua huānga.

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)

Mō te poukapa 2\times 2 \left(\begin{matrix}a&b\\c&d\end{matrix}\right), ko te ad-bc te tau whakatau.

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

Whakarūnātia.

Tāpirihia ngā kīanga tau hei kimi i te otinga whakamutunga.