解一个线性方程组。

I've been trying to solve a system of linear equations , but I didn't get this done. I hope getting an answer if it's solvable .

我一直在尝试解一个线性方程组，但我没把它做完。我希望得到一个答案，如果它是可解的。

Say we have an angle A and this system :

假设有一个角A和这个系统

y - x = sin(A)
x - z = sin(A+100) 
z - y = sin(A+200)

I'm looking for `x and y and z , the value of the angle isn't constant, but it's known ! If there is a numerical way to solve it I'll be intressed .

我在寻找x y z，这个角的值不是常数，但它是已知的!如果有一个数值方法来解决它，我将会很有兴趣。

PS: this NOT a homework. and everything I've tried is written on papers that 's the reason I didn't put here.

这不是家庭作业。我试过的每一件事都是写在纸上的，这就是我为什么不写在这里的原因。

2 个解决方案

#1

If you add all equations you get

如果你把所有的方程相加。

sin(A) + sin(A + 100) + sin(A + 200) = 0

sin(A) + sin(A + 100) + sin(A + 200) = 0。

So your system isn't solvable if the above sum is not zero. If it's zero then you have infinite solutions:

因此，如果上面的和不是零，你的系统是不能解决的。如果它是零，那么你有无穷解:

x = x, y = x + sin(A), z = x - sin(A + 100)

x = x y = x + sin(A) z = x - sin(A + 100)

where x can have any value.

其中x可以有任何值。

#2

The system can be rearranged to

系统可以重新安排。

0       = sin(A) - sin(A+100) - sin(A+200)
x - z   = sin(A+100) 
- y + z = sin(A+200)

which means that there is no solution if sin(A) - sin(A+100) - sin(A+200) != 0 holds. Otherwise, chose y at will and setting x=sin(A+100)+y and z=sin(A)-y yields a solution.

也就是说，如果sin(A) - sin(A+100) - sin(A+200) = 0，就没有解了。否则，选择y，并设置x=sin(A+100)+y和z=sin(A)-y得到一个解。

#1