Whakaoti i te {ccc}{0}&{5}&{4}{5}&{6}&{-6}{-2}&{-3}&{2}

$$\left| \begin{array} { c c c } { 0 } & { 5 } & { 4 } \\ { 5 } & { 6 } & { - 6 } \\ { - 2 } & { - 3 } & { 2 } \end{array} \right|$$

Aromātai

$$-2$$

Ngā Upane e Whakamahi ana i te Ture Sarrus

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

$$det(\left(\begin{matrix}0&5&4\\5&6&-6\\-2&-3&2\end{matrix}\right))$$

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

$$\left(\begin{matrix}0&5&4&0&5\\5&6&-6&5&6\\-2&-3&2&-2&-3\end{matrix}\right)$$

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

$$5\left(-6\right)\left(-2\right)+4\times 5\left(-3\right)=0$$

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

$$-2\times 6\times 4+2\times 5\times 5=2$$

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

$$-2$$

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).

$$det(\left(\begin{matrix}0&5&4\\5&6&-6\\-2&-3&2\end{matrix}\right))$$

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.

$$-5det(\left(\begin{matrix}5&-6\\-2&2\end{matrix}\right))+4det(\left(\begin{matrix}5&6\\-2&-3\end{matrix}\right))$$

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

$$-5\left(5\times 2-\left(-2\left(-6\right)\right)\right)+4\left(5\left(-3\right)-\left(-2\times 6\right)\right)$$

Whakarūnātia.

$$-5\left(-2\right)+4\left(-3\right)$$

Tāpirihia ngā kīanga tau hei kimi i te otinga whakamutunga.

$$-2$$

Tauwehe

$$-2$$