Whakaoti i te {lll}{2}&{3}&{4}{6}&{8}&{1}{5}&{4}&{1}

$$\left( \begin{array} { l l l } { 2 } & { 3 } & { 4 } \\ { 6 } & { 8 } & { 1 } \\ { 5 } & { 4 } & { 1 } \end{array} \right)$$

Tātai Tau Whakatau

$$-59$$

Ngā Upane e Whakamahi ana i te Ture Sarrus

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

$$det(\left(\begin{matrix}2&3&4\\6&8&1\\5&4&1\end{matrix}\right))$$

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

$$\left(\begin{matrix}2&3&4&2&3\\6&8&1&6&8\\5&4&1&5&4\end{matrix}\right)$$

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

$$2\times 8+3\times 5+4\times 6\times 4=127$$

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

$$5\times 8\times 4+4\times 2+6\times 3=186$$

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

$$127-186$$

Tango 186 mai i 127.

$$-59$$

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).

$$det(\left(\begin{matrix}2&3&4\\6&8&1\\5&4&1\end{matrix}\right))$$

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.

$$2det(\left(\begin{matrix}8&1\\4&1\end{matrix}\right))-3det(\left(\begin{matrix}6&1\\5&1\end{matrix}\right))+4det(\left(\begin{matrix}6&8\\5&4\end{matrix}\right))$$

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

$$2\left(8-4\right)-3\left(6-5\right)+4\left(6\times 4-5\times 8\right)$$

Whakarūnātia.

$$2\times 4-3+4\left(-16\right)$$

Tāpirihia ngā kīanga tau hei kimi i te otinga whakamutunga.

$$-59$$

Aromātai

$$\left(\begin{matrix}2&3&4\\6&8&1\\5&4&1\end{matrix}\right)$$