Whakaoti i te {ccc}{4}&{4}&{-2}{2}&{8}&{-4}{1}&{1}&{1}=

Aromātai

Tauwehe

Pātaitai

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

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

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-do-you-find-the-value-of-the-determinant-4-1-0-5-15-1-2-10-7

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

Tohaina

Kua tāruatia ki te papatopenga

det(\left(\begin{matrix}4&4&-2\\2&8&-4\\1&1&1\end{matrix}\right))

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

\left(\begin{matrix}4&4&-2&4&4\\2&8&-4&2&8\\1&1&1&1&1\end{matrix}\right)

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

4\times 8+4\left(-4\right)-2\times 2=12

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

8\left(-2\right)-4\times 4+2\times 4=-24

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

12-\left(-24\right)

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

Tango -24 mai i 12.

det(\left(\begin{matrix}4&4&-2\\2&8&-4\\1&1&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).

4det(\left(\begin{matrix}8&-4\\1&1\end{matrix}\right))-4det(\left(\begin{matrix}2&-4\\1&1\end{matrix}\right))-2det(\left(\begin{matrix}2&8\\1&1\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.

4\left(8-\left(-4\right)\right)-4\left(2-\left(-4\right)\right)-2\left(2-8\right)

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

4\times 12-4\times 6-2\left(-6\right)

Whakarūnātia.

Tāpirihia ngā kīanga tau hei kimi i te otinga whakamutunga.