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det(\left(\begin{matrix}5&-1&3\\0&2&-1\\5&3&1\end{matrix}\right))
Kimihia te tau whakatau o te poukapa mā te whakamahi i te tikanga hauroki.
\left(\begin{matrix}5&-1&3&5&-1\\0&2&-1&0&2\\5&3&1&5&3\end{matrix}\right)
Whakaroatia te poukapa taketake mā te tāruarua i ngā tīwae tuatahi e rua hei tīwae tuawhā me te tuarima.
5\times 2-\left(-5\right)=15
Tīmata atu i te tāurunga mauī o runga, whakareatia whakararo i ngā hauroki, ka tāpiri i ngā hua ka puta.
5\times 2\times 3+3\left(-1\right)\times 5=15
Tīmata atu i te tāurunga mauī o raro, whakareatia whakarunga i ngā hauroki, ka tāpiri i ngā hua ka puta.
15-15
Tangohia te tapeke o ngā hauroki whakarunga mai i te tapeke o ngā hua hauroki whakararo.
0
Tango 15 mai i 15.
det(\left(\begin{matrix}5&-1&3\\0&2&-1\\5&3&1\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).
5det(\left(\begin{matrix}2&-1\\3&1\end{matrix}\right))-\left(-det(\left(\begin{matrix}0&-1\\5&1\end{matrix}\right))\right)+3det(\left(\begin{matrix}0&2\\5&3\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.
5\left(2-3\left(-1\right)\right)-\left(-\left(-5\left(-1\right)\right)\right)+3\left(-5\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.
5\times 5-\left(-5\right)+3\left(-10\right)
Whakarūnātia.
0
Tāpirihia ngā kīanga tau hei kimi i te otinga whakamutunga.