Whakaoti i te {ccc}{0}&{2}&{0}{z}&{3i}&{i}{-i}&{0}&{1+i}

$$\left| \begin{array} { c c c } { 0 } & { 2 } & { 0 } \\ { z } & { 3 i } & { i } \\ { - i } & { 0 } & { 1 + i } \end{array} \right|$$

Aromātai

$$\left(-2-2i\right)z+2$$

Ngā Upane e Whakamahi ana i te Ture Sarrus

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

$$det(\left(\begin{matrix}0&2&0\\z&3i&i\\-i&0&1+i\end{matrix}\right))$$

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

$$\left(\begin{matrix}0&2&0&0&2\\z&3i&i&z&3i\\-i&0&1+i&-i&0\end{matrix}\right)$$

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

$$2i\left(-i\right)=2$$

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

$$\left(1+i\right)z\times 2=\left(2+2i\right)z$$

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

$$2-\left(2+2i\right)z$$

Tango \left(2+2i\right)z mai i 2.

$$\left(-2-2i\right)z+2$$

Ngā Upane e Whakamahi ana i te Whakaroha mā Ngā Tauriki

Kimihia te tau whakatau o te poukapa mā te whakamahi i te tikanga whakaroha ā-tauriki (te tikanga whakaroha ā-tauwehe tahi rānei).

$$det(\left(\begin{matrix}0&2&0\\z&3i&i\\-i&0&1+i\end{matrix}\right))$$

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.

$$-2det(\left(\begin{matrix}z&i\\-i&1+i\end{matrix}\right))$$

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

$$-2\left(z\left(1+i\right)-\left(-ii\right)\right)$$

Whakarūnātia.

$$-2\left(\left(1+i\right)z-1\right)$$

Tāpirihia ngā kīanga tau hei kimi i te otinga whakamutunga.

$$\left(-2-2i\right)z+2$$