MATLAB: Solve system of equations

equationsMATLABsolve

I have a system of seven equations. The equations are dependent on a variable called "Ptot". There are four constants across the equations.

I am trying to solve the seven equations to get th value of Ptot. I tried the following code but I am getting a message "Empty sym: 0-by-1".

Could you please help me?

Best Regards,

Dipen

syms Ptot P1 P2 P_vert P_horiz V H 
a=deg2rad(-37.9);       %(deg)+ve for upslope and -ve for downslope angle of shear plane
t1=deg2rad(37.9);       %(deg) angle of P1 with Horizontal
t2=deg2rad(23);         %(deg) angle of P2 with horizontal
Wc=0.74;                %(kN) Weight of concrete 
eqn1=P1==0.55*Ptot;
eqn2=P2==0.45*Ptot;
eqn3=P_vert==P1*sin(t1)+P2*sin(t2);   
eqn4=P_horiz==P1*cos(t1)+P2*cos(t2);
eqn5=V==Wc+P_vert; 
eqn6=H==P_horiz;    
eqn7=H*cos(a)-V*sin(a)==40;
eqns=[eqn7 eqn6 eqn5 eqn4 eqn3 eqn2 eqn1];
P=solve(eqns,Ptot)

Best Answer

You are asking to solve all of the equations in terms of one variable. Instead just

sol=solve(eqns) ;
P=sol.Ptot

Related Solutions

MATLAB: System of Equations: linsolve warning re: rank-deficient system, but null function & A\B aren’t helping to fix the problem.

I'm more awake now to look at your equations, although I see that use of null is still essentially meaningless here. They are all of the general form:

p1 == (Lit_IsoSr(1) - ((pOpx .* p2) + (pCpx .* p3) + (pBt .* p4)...
    + (pPl .* p5) + (pKfs .* p6) + (pQtz .* p7) + (pMt .* p8) + (pIl .* p9))) ./ pFl;

where p1, p2, p3, p4,... p9 are the unknowns. So you have a 9x9 matrix of coefficients. I wonder at first if you have values for the coefficients or not, but that is not relevant as I look at your equations.

But then, as I look more closely at your equations. Strange, that. They are all identical! You only have one equation. That is, multiply equation 1 by pFl, then re-write it, by bringing all of the terms with p1,...p9 onto the left hand side.

pFl*p1 + pOpx.*p2 + pCpx.*p3 + pBt.*p4 + pPl.*p5 + pKfs.*p6 + pQtz .* p7 + pMt.*p8 + pIl.*p9 == Lit_IsoSr(1)

Now, do the same for equation 2, multiplying by pOpx. Indeed, I get identically the same equation, with the same constant on the right hand side. If we repeat this operation on each of your equations, I get the same identical result.

VERY STRANGE.

You do NOT have a system of 9 equations in 9 unknowns. You have ONE equation, repeated 9 times. You just divided that equation by one of the constants, then decided to move some of the terms to the other side of the equality. You cannot create nine independent equations by taking your single equation, and then divide it by some value. equations 2-9 do not add any new information to the problem, beyond what you already had in equation 1.

The linear system is rank deficient because you only have ONE equation. You can completely arbitrarily pick any values you want for the unknowns p1,...p8, and then solve for p9. Or you can solve for any one of the unknowns, IF you only knew the others.

So again, this is not a probem that null can handle in any way. But worse, this is not a problem you can resolve in any meaningful way, but to write a set of 9 INDEPENDENT equations. So you do indeed need to reformulate your problem.

MATLAB: Solving a symbolic equation in one or more variables

I just changed the last two lines of your code

eqn = [a b] ==r2p(i)

sol = solve(eqn)

To view the variable sol, you can call sol.a and sol.b to call system variables in sol -> [a b] which contains [1 90] respectively

Hope this helps.

-Muthu.

Best Answer

Related Solutions

MATLAB: System of Equations: linsolve warning re: rank-deficient system, but null function & A\B aren’t helping to fix the problem.

MATLAB: Solving a symbolic equation in one or more variables

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