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

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

Tātai Tau Whakatau

$$-6$$

Ngā Upane e Whakamahi ana i te Ture Sarrus

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

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

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

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

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

$$3\times 2\left(-1\right)=-6$$

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

$$\text{true}$$

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

$$-6$$

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).

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

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.

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

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

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

Whakarūnātia.

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

Tāpirihia ngā kīanga tau hei kimi i te otinga whakamutunga.

$$-6$$

Aromātai

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