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

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

Aromātai

$$5$$

Ngā Upane e Whakamahi ana i te Ture Sarrus

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

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

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

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

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

$$-2\left(-3\right)=6$$

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

$$-3\times 3\left(-1\right)+2\left(-2\right)\times 2=1$$

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

$$6-1$$

Tango 1 mai i 6.

$$5$$

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).

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

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.

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

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

$$2\left(-2\left(-2\right)\right)-\left(-\left(-3\left(-2\right)\right)\right)-\left(-\left(-3\times 3\right)\right)$$

Whakarūnātia.

$$2\times 4-\left(-6\right)-9$$

Tāpirihia ngā kīanga tau hei kimi i te otinga whakamutunga.

$$5$$

Tauwehe

$$5$$