Whakaoti i te {lll}{18}&{-1}&{-1}{10}&{3}&{-2}{-2}&{-2}&{3}

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-2-1-3-3-0-2-1-3-0

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-value-of-the-determinant-6-3-1-0-3-3-9-0-0

https://socratic.org/questions/how-do-you-find-the-determinant-of-25-36-15-31-12-2-17-15-9

https://socratic.org/questions/how-do-you-find-the-determinant-of-0-1-4-3-2-3-8-3-4

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

Tohaina

Kua tāruatia ki te papatopenga

det(\left(\begin{matrix}18&-1&-1\\10&3&-2\\-2&-2&3\end{matrix}\right))

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

\left(\begin{matrix}18&-1&-1&18&-1\\10&3&-2&10&3\\-2&-2&3&-2&-2\end{matrix}\right)

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

18\times 3\times 3-\left(-2\left(-2\right)\right)-10\left(-2\right)=178

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

-2\times 3\left(-1\right)-2\left(-2\right)\times 18+3\times 10\left(-1\right)=48

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

178-48

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

130

Tango 48 mai i 178.

det(\left(\begin{matrix}18&-1&-1\\10&3&-2\\-2&-2&3\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).

18det(\left(\begin{matrix}3&-2\\-2&3\end{matrix}\right))-\left(-det(\left(\begin{matrix}10&-2\\-2&3\end{matrix}\right))\right)-det(\left(\begin{matrix}10&3\\-2&-2\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.

18\left(3\times 3-\left(-2\left(-2\right)\right)\right)-\left(-\left(10\times 3-\left(-2\left(-2\right)\right)\right)\right)-\left(10\left(-2\right)-\left(-2\times 3\right)\right)

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

18\times 5-\left(-26\right)-\left(-14\right)

Whakarūnātia.

130

Tāpirihia ngā kīanga tau hei kimi i te otinga whakamutunga.