Whakaoti i te {lll}{1}&{2}&{3}{1}&{1}&{0}{9}&{9}&{10}

$$\left| \begin{array} { l l l } { 1 } & { 2 } & { 3 } \\ { 1 } & { 1 } & { 0 } \\ { 9 } & { 9 } & { 10 } \end{array} \right|$$

Aromātai

$$-10$$

Ngā Upane e Whakamahi ana i te Ture Sarrus

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

$$det(\left(\begin{matrix}1&2&3\\1&1&0\\9&9&10\end{matrix}\right))$$

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

$$\left(\begin{matrix}1&2&3&1&2\\1&1&0&1&1\\9&9&10&9&9\end{matrix}\right)$$

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

$$10+3\times 9=37$$

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

$$9\times 3+10\times 2=47$$

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

$$37-47$$

Tango 47 mai i 37.

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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).

$$det(\left(\begin{matrix}1&2&3\\1&1&0\\9&9&10\end{matrix}\right))$$

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.

$$det(\left(\begin{matrix}1&0\\9&10\end{matrix}\right))-2det(\left(\begin{matrix}1&0\\9&10\end{matrix}\right))+3det(\left(\begin{matrix}1&1\\9&9\end{matrix}\right))$$

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

$$10-2\times 10+3\left(9-9\right)$$

Whakarūnātia.

$$10-2\times 10$$

Tāpirihia ngā kīanga tau hei kimi i te otinga whakamutunga.

$$-10$$

Tauwehe

$$-10$$