Whakaoti i te {lll}{i}&{j}&{k}{1}&{2}&{3}{4}&{5}&{6}

Aromātai

Pātaitai

Complex Number

5 raruraru e ōrite ana ki:

Ngā Raru Ōrite mai i te Rapu Tukutuku

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-4-6-7-3-2-4-1-1-1

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-to-calculate-this-abs-4-4-m-6-m-3-m-3-3-4

https://socratic.org/questions/how-do-you-find-the-determinant-of-8-9-3-3-5-7-1-2-4

https://math.stackexchange.com/questions/2939089/taking-signs-out-of-columns-of-matrix

Tohaina

Kua tāruatia ki te papatopenga

det(\left(\begin{matrix}i&j&k\\1&2&3\\4&5&6\end{matrix}\right))

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

\left(\begin{matrix}i&j&k&i&j\\1&2&3&1&2\\4&5&6&4&5\end{matrix}\right)

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

2i\times 6+j\times 3\times 4+k\times 5=12j+5k+12i

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

4\times 2k+5\times \left(3i\right)+6j=6j+8k+15i

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

12j+5k+12i-\left(6j+8k+15i\right)

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

6j-3k-3i

Tango 8k+15i+6j mai i 12i+12j+5k.

det(\left(\begin{matrix}i&j&k\\1&2&3\\4&5&6\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).

idet(\left(\begin{matrix}2&3\\5&6\end{matrix}\right))-jdet(\left(\begin{matrix}1&3\\4&6\end{matrix}\right))+kdet(\left(\begin{matrix}1&2\\4&5\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.

i\left(2\times 6-5\times 3\right)-j\left(6-4\times 3\right)+k\left(5-4\times 2\right)

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

-3i-j\left(-6\right)+k\left(-3\right)

Whakarūnātia.

6j-3k-3i

Tāpirihia ngā kīanga tau hei kimi i te otinga whakamutunga.