Whakaoti i te {lll}{3}&{5}&{1}{x}&{0}&{1}{-4}&{-6}&{1}

$$\left| \begin{array} { l l l } { 3 } & { 5 } & { 1 } \\ { x } & { 0 } & { 1 } \\ { - 4 } & { - 6 } & { 1 } \end{array} \right|$$

Aromātai

$$-11x-2$$

Ngā Upane e Whakamahi ana i te Ture Sarrus

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

$$det(\left(\begin{matrix}3&5&1\\x&0&1\\-4&-6&1\end{matrix}\right))$$

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

$$\left(\begin{matrix}3&5&1&3&5\\x&0&1&x&0\\-4&-6&1&-4&-6\end{matrix}\right)$$

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

$$5\left(-4\right)+x\left(-6\right)=-6x-20$$

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

$$-6\times 3+x\times 5=5x-18$$

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

$$-6x-20-\left(5x-18\right)$$

Tango -18+5x mai i -20-6x.

$$-11x-2$$

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).

$$det(\left(\begin{matrix}3&5&1\\x&0&1\\-4&-6&1\end{matrix}\right))$$

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.

$$3det(\left(\begin{matrix}0&1\\-6&1\end{matrix}\right))-5det(\left(\begin{matrix}x&1\\-4&1\end{matrix}\right))+det(\left(\begin{matrix}x&0\\-4&-6\end{matrix}\right))$$

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

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

Whakarūnātia.

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

Tāpirihia ngā kīanga tau hei kimi i te otinga whakamutunga.

$$-11x-2$$

Whātahi e ai ki x

$$-\frac{11x^{2}}{2}-2x+С$$