MATLAB: Determining particular solution of 3×3 matrix using variation of parameters

Question

If I am correct in my process for variation of parameters for a matrix:

I already have my general solution that was solved (with some help…thanks!) via undetermined coefficients.

I then need to take the inverse of that matrix.

Then I multiply the inverse by the non-homogeneous part of the equation. And this is where I get stuck…

I can then take the integral of the resulting matrix for my particular solution…

Is taking this approach flawed in general? Or is there something simple that I am missing when I try to multiply the inverse by the non-hom. part?

Thank you for any insight.

Here is my general solution:

>>  null(evs(1)*Id3-A)
 
 
ans =
 
 152/21
  -57/7
      1
      
>> null(evs(2)*Id3-A)
 
ans =
 
    0
 -1/7
    1
    
    
>> null(evs(3)*Id3-A)
 
ans =
 
 0
 0
 1
 

And this is where the trouble begins…

 
 
 >> A = sym([152/21,0,0;-57/7,-1/7,0;0,0,1]);
>> Y=inv(A)
 
Y =
 
[ 21/152,  0, 0]
[  -63/8, -7, 0]
[      0,  0, 1]
 
>> B = sym([-1575,0,0]);
>> Y*B
??? Error using ==> mupadmex
Error in MuPAD command: dimensions do not match [(Dom::Matrix(Dom::ExpressionField()))::_mult2]
Error in ==> sym.sym>sym.mtimes at 180
            X = mupadmex('mllib::mtimes',A.s,B.s);
 

Answer 1

Remove sym()