Whakaoti i te {ccc}{1}&{3}&{-1}{0}&{-1}&{3}{4}&{3}&{5}

$$\left| \begin{array} { c c c } { 1 } & { 3 } & { - 1 } \\ { 0 } & { - 1 } & { 3 } \\ { 4 } & { 3 } & { 5 } \end{array} \right|$$

Aromātai

$$18$$

Ngā Upane e Whakamahi ana i te Ture Sarrus

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

$$det(\left(\begin{matrix}1&3&-1\\0&-1&3\\4&3&5\end{matrix}\right))$$

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

$$\left(\begin{matrix}1&3&-1&1&3\\0&-1&3&0&-1\\4&3&5&4&3\end{matrix}\right)$$

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

$$-5+3\times 3\times 4=31$$

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

$$4\left(-1\right)\left(-1\right)+3\times 3=13$$

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

$$31-13$$

Tango 13 mai i 31.

$$18$$

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).

$$det(\left(\begin{matrix}1&3&-1\\0&-1&3\\4&3&5\end{matrix}\right))$$

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.

$$det(\left(\begin{matrix}-1&3\\3&5\end{matrix}\right))-3det(\left(\begin{matrix}0&3\\4&5\end{matrix}\right))-det(\left(\begin{matrix}0&-1\\4&3\end{matrix}\right))$$

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

$$-5-3\times 3-3\left(-4\times 3\right)-\left(-4\left(-1\right)\right)$$

Whakarūnātia.

$$-14-3\left(-12\right)-4$$

Tāpirihia ngā kīanga tau hei kimi i te otinga whakamutunga.

$$18$$

Tauwehe

$$2\times 3^{2}$$