Whakaoti i te {l}{3a+4b=4lambda}{4lambda+3a=6}{3b+4lambda=3}

$$\left. \begin{array} { l } { 3 a + 4 b = 4 \lambda } \\ { 4 \lambda + 3 a = 6 } \\ { 3 b + 4 \lambda = 3 } \end{array} \right.$$

Whakaoti mō a, b, λ

$$a=1$$

$$b=0$$

$$\lambda =\frac{3}{4}=0.75$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te 3a+4b=4\lambda mō a.

$$a=-\frac{4}{3}b+\frac{4}{3}\lambda$$

Whakakapia te -\frac{4}{3}b+\frac{4}{3}\lambda mō te a i te whārite 4\lambda +3a=6.

$$4\lambda +3\left(-\frac{4}{3}b+\frac{4}{3}\lambda \right)=6$$

Me whakaoti te whārite tuarua mō b me te whārite tuatoru mō \lambda .

$$b=-\frac{3}{2}+2\lambda \lambda =\frac{3}{4}-\frac{3}{4}b$$

Whakakapia te -\frac{3}{2}+2\lambda mō te b i te whārite \lambda =\frac{3}{4}-\frac{3}{4}b.

$$\lambda =\frac{3}{4}-\frac{3}{4}\left(-\frac{3}{2}+2\lambda \right)$$

Me whakaoti te \lambda =\frac{3}{4}-\frac{3}{4}\left(-\frac{3}{2}+2\lambda \right) mō \lambda .

$$\lambda =\frac{3}{4}$$

Whakakapia te \frac{3}{4} mō te \lambda i te whārite b=-\frac{3}{2}+2\lambda .

$$b=-\frac{3}{2}+2\times \frac{3}{4}$$

Tātaitia te b i te b=-\frac{3}{2}+2\times \frac{3}{4}.

$$b=0$$

Whakakapia te 0 mō te b me te \frac{3}{4} mō \lambda i te whārite a=-\frac{4}{3}b+\frac{4}{3}\lambda .

$$a=-\frac{4}{3}\times 0+\frac{4}{3}\times \frac{3}{4}$$

Tātaitia te a i te a=-\frac{4}{3}\times 0+\frac{4}{3}\times \frac{3}{4}.

$$a=1$$

Kua oti te pūnaha te whakatau.

$$a=1 b=0 \lambda =\frac{3}{4}$$