Solve fails to find a solution for trivial linear system
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I'm trying to find the value of G in the following set of equations by code:
clear all; clc;
syms R T S u yr y B A G
eq1 = R*u == T*yr - S*y;
eq2 = y == (B/A)*u;
eq3 = y == G*yr;
solve([eq1,eq2,eq3], G)
However, solve fails with an empty solution set, although this system has a trivial answer.
It's easy to see how it can be done, from eq1:
u == (T*yr - S*y)/R
From eq2:
y == (B/A)*(T*yr - S*y)/R
Thus:
y = yr*(B*T)/(A*R + B*S)
Finally, from eq3:
G = (B*T)/(A*R + B*S)
I can't understand why solve fails in this case. I appreciate any help I can get.
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채택된 답변
Walter Roberson
2016년 3월 6일
Actually it is just a matter of telling it all three variables to solve for:
solve(eq1, eq2, eq3, y, u, G)
댓글 수: 2
Walter Roberson
2016년 3월 6일
When you do not specify the other variables, the best you could have hoped for was that G was returned as y/yr, from the third equation, as it would have had no reason to know which other variables to eliminate.
추가 답변 (1개)
Star Strider
2016년 3월 6일
Sometimes, you have to lead it gently by the hand:
syms R T S u yr y B A G
eq1 = R*u == T*yr - S*y;
eq2 = y == (B/A)*u;
eq3 = y == G*yr;
eq4 = solve(eq2, eq3);
yr = eq4.yr;
eq5 = subs(eq1, yr);
G_solved = solve(eq5, G)
G_solved =
-(B*S*u)/(A*(R*u - T*yr))
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