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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.