Whakaoti i te {lll}{2}&{8}&{-3}{3}&{9}&{6}{6}&{1}&{0}

$$\left( \begin{array} { l l l } { 2 } & { 8 } & { - 3 } \\ { 3 } & { 9 } & { 6 } \\ { 6 } & { 1 } & { 0 } \end{array} \right)$$

Tātai Tau Whakatau

$$429$$

Ngā Upane e Whakamahi ana i te Ture Sarrus

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

$$det(\left(\begin{matrix}2&8&-3\\3&9&6\\6&1&0\end{matrix}\right))$$

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

$$\left(\begin{matrix}2&8&-3&2&8\\3&9&6&3&9\\6&1&0&6&1\end{matrix}\right)$$

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

$$8\times 6\times 6-3\times 3=279$$

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

$$6\times 9\left(-3\right)+6\times 2=-150$$

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

$$279-\left(-150\right)$$

Tango -150 mai i 279.

$$429$$

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).

$$det(\left(\begin{matrix}2&8&-3\\3&9&6\\6&1&0\end{matrix}\right))$$

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.

$$2det(\left(\begin{matrix}9&6\\1&0\end{matrix}\right))-8det(\left(\begin{matrix}3&6\\6&0\end{matrix}\right))-3det(\left(\begin{matrix}3&9\\6&1\end{matrix}\right))$$

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

$$2\left(-6\right)-8\left(-6\times 6\right)-3\left(3-6\times 9\right)$$

Whakarūnātia.

$$2\left(-6\right)-8\left(-36\right)-3\left(-51\right)$$

Tāpirihia ngā kīanga tau hei kimi i te otinga whakamutunga.

$$429$$

Aromātai

$$\left(\begin{matrix}2&8&-3\\3&9&6\\6&1&0\end{matrix}\right)$$