Determining particular solution of 3x3 matrix using variation of parameters

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

[madhan ravi]

Remove sym()

[spcrooks]

Thanks for the response, madhan. Yes...here I am again.

I removed "sym()" but ran into the following error.

Do I need a different form for this matrix multiplication?

>> A = [152/21,0,0;-57/7,-1/7,0;0,0,1];
>> Y = inv(A)

Y =

    0.1382   -0.0000         0
   -7.8750   -7.0000         0
         0         0    1.0000

>> B = [-1575,0,0];
>> Y*B
??? Error using ==> mtimes
Inner matrix dimensions must agree.

[madhan ravi]

Don't forget the rule for matrix multiplication:

Y*B.' % 3 by 3 times 3 by 1

[spcrooks]

How silly...big difference between [-1575,0,0] and [-1575;0;0] !

Got it. Thanks, again.

[madhan ravi]

Anytime :) , Human errors , you will improve don’t worry .