Inverse Matrix for 6x6 matrix with variables

I am trying to find the inverse of the matrix above. Here is my code:

x = symvar('x')
y = symvar('y')
z = symvar ('z')
A=[x y y 0 0 0; y x y 0 0 0; y y x 0 0 0; 0 0 0 z 0 0; 0 0 0 0 z 0; 0 0 0 0 0 z]
b=inv(A)

This is giving me the following error:

Error using inv

Invalid data type. Input matrix must be double or single.

Error in untitled (line 5)

b=inv(A)

Could someone explain to me what I'm doing wrong? I'm fairly inexperienced with matlab and I'm not sure what is wrong. Any information is greatly appreciated. Thank you!

Answer 1

[Stephen23]

syms x y z
A = [x,y,y,0,0,0; y,x,y,0,0,0; y,y,x,0,0,0; 0,0,0,z,0,0; 0,0,0,0,z,0; 0,0,0,0,0,z];
b = inv(A)

b = 

[Luis]

Copying and pasting your code is still giving me errors. Could it be something with my software? I haven't updated to the latest version of Matlab

[John D'Errico]

@Luis

You may have written a function of your own, named inv. That would be a truly terrible idea.

[James Tursa]

@Luis Type this at the command line:

which inv

Answer 2

[Steven Lord]

The symvar function does not define symbolic variables. It identifies identifiers in an expression (other than those in a small list of excluded identifiers) that could be variables and returns those identifiers in a cell array of text data.

x = symvar('x')

x = 1×1 cell array
    {'x'}

y = symvar('y')

y = 1×1 cell array
    {'y'}

z = symvar ('z')

z = 1×1 cell array
    {'z'}

So when you construct A, it is not a symbolic variable. It's a cell array.

A=[x y y 0 0 0; y x y 0 0 0; y y x 0 0 0; 0 0 0 z 0 0; 0 0 0 0 z 0; 0 0 0 0 0 z]

A = 6×6 cell array
    {'x'}    {'y'}    {'y'}    {[0]}    {[0]}    {[0]}
    {'y'}    {'x'}    {'y'}    {[0]}    {[0]}    {[0]}
    {'y'}    {'y'}    {'x'}    {[0]}    {[0]}    {[0]}
    {[0]}    {[0]}    {[0]}    {'z'}    {[0]}    {[0]}
    {[0]}    {[0]}    {[0]}    {[0]}    {'z'}    {[0]}
    {[0]}    {[0]}    {[0]}    {[0]}    {[0]}    {'z'}

whos x y z A

  Name      Size            Bytes  Class    Attributes

  A         6x6              3960  cell               
  x         1x1               106  cell               
  y         1x1               106  cell               
  z         1x1               106  cell               

Because of this the error message is correct. The inv function is not defined for cell arrays.

Instead, you should use the sym or syms functions to define symbolic variables (as shown in the answer from @Stephen23) and create A using those symbolic variables.

syms x y z
A=[x y y 0 0 0; y x y 0 0 0; y y x 0 0 0; 0 0 0 z 0 0; 0 0 0 0 z 0; 0 0 0 0 0 z]

A = 

whos x y z A

  Name      Size            Bytes  Class    Attributes

  A         6x6                 8  sym                
  x         1x1                 8  sym                
  y         1x1                 8  sym                
  z         1x1                 8  sym                

The inv function is defined for sym arrays.

AI = inv(A)

AI = 

The fact that the symvar function you called didn't display anything makes me suspect that you might be using a symvar.m file other than the ones in MATLAB, Symbolic Math Toolbox, or Curve Fitting Toolbox. Or did you simply not show us the output that you received when you ran the code? What does this command show you when you run it?

which -all symvar

/MATLAB/toolbox/matlab/funfun/symvar.m
/MATLAB/toolbox/symbolic/symbolic/@sym/symvar.m      % sym method
/MATLAB/toolbox/matlab/funfun/@inline/symvar.m       % inline method
/MATLAB/toolbox/curvefit/curvefit/@fittype/symvar.m  % fittype method