Whakaoti i te {ccc}{1}&{-18}&{-11}{3}&{6}&{-4}{13}&{8}&{3}

$$\left| \begin{array} { c c c } { 1 } & { - 18 } & { - 11 } \\ { 3 } & { 6 } & { - 4 } \\ { 13 } & { 8 } & { 3 } \end{array} \right|$$

Aromātai

$$1742$$

Ngā Upane e Whakamahi ana i te Ture Sarrus

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

$$det(\left(\begin{matrix}1&-18&-11\\3&6&-4\\13&8&3\end{matrix}\right))$$

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

$$\left(\begin{matrix}1&-18&-11&1&-18\\3&6&-4&3&6\\13&8&3&13&8\end{matrix}\right)$$

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

$$6\times 3-18\left(-4\right)\times 13-11\times 3\times 8=690$$

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

$$13\times 6\left(-11\right)+8\left(-4\right)+3\times 3\left(-18\right)=-1052$$

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

$$690-\left(-1052\right)$$

Tango -1052 mai i 690.

$$1742$$

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).

$$det(\left(\begin{matrix}1&-18&-11\\3&6&-4\\13&8&3\end{matrix}\right))$$

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.

$$det(\left(\begin{matrix}6&-4\\8&3\end{matrix}\right))-\left(-18det(\left(\begin{matrix}3&-4\\13&3\end{matrix}\right))\right)-11det(\left(\begin{matrix}3&6\\13&8\end{matrix}\right))$$

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

$$6\times 3-8\left(-4\right)-\left(-18\left(3\times 3-13\left(-4\right)\right)\right)-11\left(3\times 8-13\times 6\right)$$

Whakarūnātia.

$$50-\left(-18\times 61\right)-11\left(-54\right)$$

Tāpirihia ngā kīanga tau hei kimi i te otinga whakamutunga.

$$1742$$

Tauwehe

$$2\times 13\times 67$$