How to Solve sytem of 7 equations with 6 unknown variables? How to combine any two equations? equations and variables given belowRequest for help
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Vijaya Kumar Kondagunta
on 27 Jun 2021
Commented: Vijaya Kumar Kondagunta
on 30 Jun 2021
format short
syms eqn1 eqn2 eqn3 eqn4 eqn5 eqn6 eqn7 eqns sol p1sol p2sol p3sol p4sol p5sol p6sol p1 p2 p3 p4 p5 p6
eqn1 = -p1*0.00074+p2*30+ p5*2 + p6*0.2 == 0
eqn2 = p1*0.00062 - p2*30.00077 == 0;
eqn3 = p1*0.00012 +0.00031*p2 - p3*0.00012 == 0;
eqn4 = p2*0.00046 +p3*0.00012- p4*0.00063 == 0;
eqn5 = p4*0.0004 - p5*2 == 0;
eqn6 = p4*0.00023 - p6*0.2 == 0;
eqn7 = p1+p2+p3+p4+p5+p6==1;
% p1 to p6 above are 6 varaibles with 7 equations
% ? eqns = [eqn1, eqn2, eqn3, eqn4, eqn5, eqn7]
% ? sol = solve([eqns],[p1,p2,p3,p4,p5,p6]);
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Accepted Answer
David Goodmanson
on 28 Jun 2021
Hello Vijaya,
This is an overdetermined set of linear equations of the form M*x = b and can be solved in the least squares sense with the backslash function. The matrix M is (if I have not made a mistake)
M = [-0.00074 30 0 0 2 0.2
0.00062 -30.00077 0 0 0 0
0.00012 0.00031 -0.00012 0 0 0
0 0.00046 0.00012 -0.00063 0 0
0 0 0 0.0004 -2 0
0 0 0 0.00023 0 -0.2
1 1 1 1 1 1 ]
cond(M)
ans = 2.2943e+05
The condition number is large but not unreasonable. Then
b = [0 0 0 0 0 0 1]';
format short g
x = M\b
x =
0.45645
9.433e-06
0.45647
0.086954
1.7391e-05
9.9997e-05
concistency_check = M*x % compare with b
concistency_check =
1.2769e-17
7.3885e-18
-3.6135e-17
1.0916e-18
1.3783e-17
1.119e-18
1
This result is not so bad.
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