Whakaoti i te {lll}{1}&{a}&{d}{1}&{b}&{d}{1}&{c}&{d}

$$\left| \begin{array} { l l l } { 1 } & { a } & { d } \\ { 1 } & { b } & { d } \\ { 1 } & { c } & { d } \end{array} \right|$$

Aromātai

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Ngā Upane e Whakamahi ana i te Ture Sarrus

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

$$det(\left(\begin{matrix}1&a&d\\1&b&d\\1&c&d\end{matrix}\right))$$

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

$$\left(\begin{matrix}1&a&d&1&a\\1&b&d&1&b\\1&c&d&1&c\end{matrix}\right)$$

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

$$bd+ad+dc=d\left(a+b+c\right)$$

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

$$bd+cd+da=d\left(a+b+c\right)$$

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

$$d\left(a+b+c\right)-d\left(a+b+c\right)$$

Tango d\left(b+a+c\right) mai i d\left(b+a+c\right).

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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).

$$det(\left(\begin{matrix}1&a&d\\1&b&d\\1&c&d\end{matrix}\right))$$

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.

$$det(\left(\begin{matrix}b&d\\c&d\end{matrix}\right))-adet(\left(\begin{matrix}1&d\\1&d\end{matrix}\right))+ddet(\left(\begin{matrix}1&b\\1&c\end{matrix}\right))$$

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

$$bd-cd-a\left(d-d\right)+d\left(c-b\right)$$

Whakarūnātia.

$$d\left(b-c\right)+d\left(c-b\right)$$

Tāpirihia ngā kīanga tau hei kimi i te otinga whakamutunga.

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Tauwehe

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