Whakaoti i te {ccc}{1}&{3}&{1}{2}&{0}&{4}{-1}&{-3}&{-3}

$$\left( \begin{array} { c c c } { 1 } & { 3 } & { 1 } \\ { 2 } & { 0 } & { 4 } \\ { - 1 } & { - 3 } & { - 3 } \end{array} \right)$$

Tātai Tau Whakatau

$$12$$

Ngā Upane e Whakamahi ana i te Ture Sarrus

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

$$det(\left(\begin{matrix}1&3&1\\2&0&4\\-1&-3&-3\end{matrix}\right))$$

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

$$\left(\begin{matrix}1&3&1&1&3\\2&0&4&2&0\\-1&-3&-3&-1&-3\end{matrix}\right)$$

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

$$3\times 4\left(-1\right)+2\left(-3\right)=-18$$

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

$$-3\times 4-3\times 2\times 3=-30$$

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

$$-18-\left(-30\right)$$

Tango -30 mai i -18.

$$12$$

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).

$$det(\left(\begin{matrix}1&3&1\\2&0&4\\-1&-3&-3\end{matrix}\right))$$

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.

$$det(\left(\begin{matrix}0&4\\-3&-3\end{matrix}\right))-3det(\left(\begin{matrix}2&4\\-1&-3\end{matrix}\right))+det(\left(\begin{matrix}2&0\\-1&-3\end{matrix}\right))$$

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

$$-\left(-3\times 4\right)-3\left(2\left(-3\right)-\left(-4\right)\right)+2\left(-3\right)$$

Whakarūnātia.

$$12-3\left(-2\right)-6$$

Tāpirihia ngā kīanga tau hei kimi i te otinga whakamutunga.

$$12$$

Aromātai

$$\left(\begin{matrix}1&3&1\\2&0&4\\-1&-3&-3\end{matrix}\right)$$