Whakaoti i te {lll}{1}&{0}&{2}{1}&{3}&{4}{0}&{6}&{0}

$$\left( \begin{array} { l l l } { 1 } & { 0 } & { 2 } \\ { 1 } & { 3 } & { 4 } \\ { 0 } & { 6 } & { 0 } \end{array} \right)$$

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.

$$det(\left(\begin{matrix}1&0&2\\1&3&4\\0&6&0\end{matrix}\right))$$

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

$$\left(\begin{matrix}1&0&2&1&0\\1&3&4&1&3\\0&6&0&0&6\end{matrix}\right)$$

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

$$2\times 6=12$$

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

$$6\times 4=24$$

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

$$12-24$$

Tango 24 mai i 12.

$$-12$$

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).

$$det(\left(\begin{matrix}1&0&2\\1&3&4\\0&6&0\end{matrix}\right))$$

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.

$$det(\left(\begin{matrix}3&4\\6&0\end{matrix}\right))+2det(\left(\begin{matrix}1&3\\0&6\end{matrix}\right))$$

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

$$-6\times 4+2\times 6$$

Whakarūnātia.

$$-24+2\times 6$$

Tāpirihia ngā kīanga tau hei kimi i te otinga whakamutunga.

$$-12$$

Aromātai

$$\left(\begin{matrix}1&0&2\\1&3&4\\0&6&0\end{matrix}\right)$$