topic 3 equations 3 Unknown values in Mathcad

3 equations 3 Unknown values

ptc-4476859 — Thu, 03 May 2018 17:21:07 GMT

Hello,I'm trying to solve for 3 values, having 3 equations,See attached file Thnaks in advance for your help!

Re: 3 equations 3 Unknown values

Werner_E — Fri, 19 Apr 2013 19:09:17 GMT

1) You had a multiplication sign between Find and the vector of variables Ri

2) Using a solve block with numeric evaluation will require you to provide guess values for the solved for variables. (For reasons I can't explain symbolic evaluation of Find will return wrong results, even if the units are omitted)

Re: 3 equations 3 Unknown values

Werner_E — Fri, 19 Apr 2013 19:28:18 GMT

Correction: Symbolic evaluation without units will give you a solution (I got confused with N and lbf), but a different one, as your system has no unique solution.

Symbolic eval with units returns a solution vector with zeros, which is wrong - don't know why

Re: 3 equations 3 Unknown values

ValeryOchkov — Sun, 21 Apr 2013 11:53:05 GMT

Dennis Lopez wrote:
Hello,
I'm trying to solve for 3 values, having 3 equations,

Show please the picture of your forces.

Re: 3 equations 3 Unknown values

lvl107 — Sun, 21 Apr 2013 16:50:19 GMT

It seem to be like so:

Best Regards.

Re: 3 equations 3 Unknown values

Werner_E — Sun, 21 Apr 2013 17:49:50 GMT

No need to calculate the reduced row echolon form manually, you may use rref.

But as rank(M)=rank(ME)=2<3 we already know, that we have an infinite number of solutions. You may google "Rouché-Capelli theorem".

Strange enough symbolic evaluation will yield wrong result!!?? Probably the result of numerical inaccuracy due to the awful automatic switch to float mode.

Re: 3 equations 3 Unknown values

lvl107 — Sun, 21 Apr 2013 18:26:08 GMT

rref( ) function sometimes works sometimes doesn't :

Best Regards.

Re: 3 equations 3 Unknown values

Werner_E — Sun, 21 Apr 2013 18:43:55 GMT

Looks like there is a bug in your version (14, if I remember correct).

This is what Mathcad 15 M020 comes up with:

Re: 3 equations 3 Unknown values

lvl107 — Sun, 21 Apr 2013 20:32:35 GMT

I have only Mathcad 14. By the way, and could you do me a favor, give a sreenshot of :

in Mathcad 15 M020. Thanks.

Re: 3 equations 3 Unknown values

Werner_E — Sun, 21 Apr 2013 20:55:31 GMT

I get the same (wrong) result as you. Thats what happens quite often with numeric methods. The symbolics would refuse to evaluate that expression (with an inappropriate error messoge, though).

But why would you use lsolve on a system of equations which clearly has no solution (different rank for coefficient matrix and augmented matrix)?

Again you would see numeric inaccuracy if you evaluate the determinant numerically.

BTW, you could install the 30 day eval of Mathcad 15 on a spare computer, if you have that oportunity or in a VM, or use Mathcad Prime2 Express parallel with your MC14. Express won't let you do symbolic operation and solve blocks after its 30 day trial period. Numeric evals should work.