Solving An Equation - Linear Algebra

Hello,

I would like to solve the following equation:

eqn = Ff == Kff*uf + Kfs*us; % I want to solve for uf knowing that

Kff =

3.0240 0.7680

0.7680 3.2427

Kfs =

0 0 -1.0240 -0.7680 -2.0000 0

0 -2.6667 -0.7680 -0.5760 0 0

Ff =

0

0

us =

0

-25

0

0

0

0

The problem is that I'm getting an error from MATLAB saying that uf is not defined, uf is supposed to be a 2x1 matrix but I want to solve for it. How can I do that?

Answer 1

[Star Strider]

Straightforward:

KFF = Kff \ -(Kfs*us)
KFF =
     5.5556
    -21.8750

Another option is to use fsolve:

[UF, fval] = fsolve(@(uf) Kff*uf + Kfs*us, [1; 1])

UF =
     5.5556
   -21.8750


fval =
    -7.1054e-015
   -14.2109e-015
   

[Hazem El Sankari]

Thank you!

But what does [1; 1] refer to at the end of the function?

[Hazem El Sankari]

Also, what Ff was, say, [100 ; 200]?

How can the equation be adjusted as then?

[Star Strider]

My pleasure.

‘But what does [1; 1] refer to at the end of the function?’

The ‘[1;1]’ is an initial parameter estimate. The fsolve function needs to have an initial guess at the value to solve for.

‘Also, what Ff was, say, [100 ; 200]?’

Ff = [100; 200]

[UF, fval] = fsolve(@(uf) Kff*uf + Kfs*us - Ff, [1; 1])

Kfsus = Kfs*us;
UF = Kff \ -((Kfs*us) - Ff)

yield respectively:

UF =

   24.0742
   35.4160


fval =

     0
     0


UF =

  24.0742
  35.4160

[Hazem El Sankari]

Thanks again for your quick and helpful reply!

[Star Strider]

My pleasure.

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