Whakaoti i te {ccc}{4}&{-10}&{2}{-10}&{14}&{26}{2}&{26}&{-34}

$$\left| \begin{array} { c c c } { 4 } & { - 10 } & { 2 } \\ { - 10 } & { 14 } & { 26 } \\ { 2 } & { 26 } & { - 34 } \end{array} \right|$$

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.

$$det(\left(\begin{matrix}4&-10&2\\-10&14&26\\2&26&-34\end{matrix}\right))$$

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

$$\left(\begin{matrix}4&-10&2&4&-10\\-10&14&26&-10&14\\2&26&-34&2&26\end{matrix}\right)$$

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

$$4\times 14\left(-34\right)-10\times 26\times 2+2\left(-10\right)\times 26=-2944$$

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

$$2\times 14\times 2+26\times 26\times 4-34\left(-10\right)\left(-10\right)=-640$$

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

$$-2944-\left(-640\right)$$

Tango -640 mai i -2944.

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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).

$$det(\left(\begin{matrix}4&-10&2\\-10&14&26\\2&26&-34\end{matrix}\right))$$

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.

$$4det(\left(\begin{matrix}14&26\\26&-34\end{matrix}\right))-\left(-10det(\left(\begin{matrix}-10&26\\2&-34\end{matrix}\right))\right)+2det(\left(\begin{matrix}-10&14\\2&26\end{matrix}\right))$$

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

$$4\left(14\left(-34\right)-26\times 26\right)-\left(-10\left(-10\left(-34\right)-2\times 26\right)\right)+2\left(-10\times 26-2\times 14\right)$$

Whakarūnātia.

$$4\left(-1152\right)-\left(-10\times 288\right)+2\left(-288\right)$$

Tāpirihia ngā kīanga tau hei kimi i te otinga whakamutunga.

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Tauwehe

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