equationsToMatrix and linsolve giving incorrect results for voltage divider

Question

Tfm tfm 2016-10-23

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/308736-equationstomatrix-and-linsolve-giving-incorrect-results-for-voltage-divider

编辑： Walter Roberson 2016-10-23

采纳的回答： John D'Errico

在 MATLAB Online 中打开

I need the solutions for r1, r2 and r3 for the following voltage divider:

Hence the following eqs. system arise:

eq1=(r1+r2+r3)/(1e5+r1+r2+r3)==0.238
eq2=(r2+r3)/(1e5+r1+r2+r3)==0.213
eq3=(r3)/(1e5+r1+r2+r3)==0.125

1) [A,B] = equationsToMatrix([eq1,eq2,eq3], [r1,r2,r3]) gives the error: "Cannot convert to matrix form because the system does not seem to be linear." It seems linear to me, what am I missing?

2) I made step 1 by hand, and found A*X=Y leading to:

A = [-.875 -.875 .875, -.787 .787 .787, .762 .762 .762]
X=[r1, r2, r3]

and

Y=[12.5e3, 21.3e3, 23.8e3]

Then linsolve(A,Y) gives:

ans =

However this answer is wrong. If I enter these values in a simulation, I don't get, i.e., 0.125*Vs over R3. What am I missing again??

3) I found the correct answer using solve instead of linsolve:

[x1, x2, x3]=solve(eq1,eq2,eq3)

Gives after vpa():

x1 = 3281
x2 = 115448
x3 = 16404

And those values run fine during simulation. I still don't get 1) and 2) though.

Also seems like hitting enter while typing won't space between lines!!

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Answer 1

John D'Errico 2016-10-23

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https://ww2.mathworks.cn/matlabcentral/answers/308736-equationstomatrix-and-linsolve-giving-incorrect-results-for-voltage-divider#answer_240300

在 MATLAB Online 中打开

Is this a linear equation in x and y?

x/y = a

NO. It is not. Perhaps you think you can transform it to a linear equation, simply by multiplying by y, to yield

x = y*a

NOT true. The two equations simply are not the same, because if y=0, that implies x=0 in the latter case, whereas (x,y) = (0,0) is NOT a valid solution to the original equation.

So MATLAB told you those equations are not in fact linear, which is the fact.

Now, suppose we decide that (1e5 + r1 + r2 + r3) will NEVER be zero.

syms r1 r2 r3
eq1=(r1+r2+r3) == (1e5+r1+r2+r3)*0.238;
eq2=(r2+r3) == (1e5+r1+r2+r3)*0.213;
eq3=(r3) == (1e5+r1+r2+r3)*0.125;
[A,b] = equationsToMatrix(eq1,eq2,eq3)
A =
[   381/500,  381/500,  381/500]
[ -213/1000, 787/1000, 787/1000]
[      -1/8,     -1/8,      7/8]
b =
 23800
 21300
 12500

... which is not what you wrote. So you need to check your algebra. And you need to remember what they surely taught you some years ago in algebra 1 about the dangers of multiplying by zero.