Whakaoti i te {rrr}{2}&{-1}&{1}{1}&{1}&{1}{-1}&{1}&{5}

$$\left| \begin{array} { r r r } { 2 } & { - 1 } & { 1 } \\ { 1 } & { 1 } & { 1 } \\ { - 1 } & { 1 } & { 5 } \end{array} \right|$$

Aromātai

$$16$$

Ngā Upane e Whakamahi ana i te Ture Sarrus

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

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

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

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

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

$$2\times 5-\left(-1\right)+1=12$$

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

$$-1+2+5\left(-1\right)=-4$$

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

$$12-\left(-4\right)$$

Tango -4 mai i 12.

$$16$$

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).

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

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.

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

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

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

Whakarūnātia.

$$2\times 4-\left(-6\right)+2$$

Tāpirihia ngā kīanga tau hei kimi i te otinga whakamutunga.

$$16$$

Tauwehe

$$2^{4}$$