Whakaoti i te {lll}{2}&{5}&{2}{3}&{2}&{1}{4}&{3}&{1}

$$\left( \begin{array} { l l l } { 2 } & { 5 } & { 2 } \\ { 3 } & { 2 } & { 1 } \\ { 4 } & { 3 } & { 1 } \end{array} \right)$$

Tātai Tau Whakatau

$$5$$

Ngā Upane e Whakamahi ana i te Ture Sarrus

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

$$det(\left(\begin{matrix}2&5&2\\3&2&1\\4&3&1\end{matrix}\right))$$

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

$$\left(\begin{matrix}2&5&2&2&5\\3&2&1&3&2\\4&3&1&4&3\end{matrix}\right)$$

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

$$2\times 2+5\times 4+2\times 3\times 3=42$$

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

$$4\times 2\times 2+3\times 2+3\times 5=37$$

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

$$42-37$$

Tango 37 mai i 42.

$$5$$

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).

$$det(\left(\begin{matrix}2&5&2\\3&2&1\\4&3&1\end{matrix}\right))$$

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.

$$2det(\left(\begin{matrix}2&1\\3&1\end{matrix}\right))-5det(\left(\begin{matrix}3&1\\4&1\end{matrix}\right))+2det(\left(\begin{matrix}3&2\\4&3\end{matrix}\right))$$

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

$$2\left(2-3\right)-5\left(3-4\right)+2\left(3\times 3-4\times 2\right)$$

Whakarūnātia.

$$2\left(-1\right)-5\left(-1\right)+2$$

Tāpirihia ngā kīanga tau hei kimi i te otinga whakamutunga.

$$5$$

Aromātai

$$\left(\begin{matrix}2&5&2\\3&2&1\\4&3&1\end{matrix}\right)$$