the inverse of a symbolic matrix using inv is not correct

I am trying to calculate the incerse of a matrix symbolically, I am using the command inv that matlab suggest, when i try with the following code to multiply sigma times their inverse i have the identity matrixm and that is telling me the inverse is ok.

b1 = sym('b1');
b2 = sym('b2');
c = sym('c');
psi = sym('psi');
K=sym('K');
N1=sym('N1');
N2=sym('N2');
r=sym('r');
mu1=sym('mu1');
mu2=sym('mu2');
rho=sym('rho');
q=sym('q');
a1=sym('a1');
a2=sym('a2');

T=[b1+K*N1  r*K*N1; c*psi*q*N2 b2];

sigma11= mu1+a1+psi*q*N2;
sigma12=0;
sigma21=0;
sigma22= mu2+a2;

sigma=[sigma11 sigma12; sigma21 sigma22];
sigmainverse=inv(sigma);  

times=sigma*sigmainverse

I have as output the identity so is great. The problem is that when I do the same thing with a different matrices I have a different output (not the identitiy), what am I doing wrong? Here is the code:

b11 = sym('b11');
b22 = sym('b22');
b12 = sym('b12');
b21 = sym('b21');
K1=sym('K1');
K2=sym('K2');
N1=sym('N1');
N2=sym('N2');
r1=sym('r1');
r2=sym('r2');
mu1=sym('mu1');
mu2=sym('mu2');
a12=sym('a12');
a21=sym('a21');
rho=sym('rho');

T=[b11 0; 0 b22];

sigma11= -mu1-r1*N1/K1-r1*a12*N2/K1;
sigma12=b12;
sigma21=b21;
sigma22= -mu2-r2*N2/K2-r2*a21*N1/K2;

sigmaok=[sigma11 sigma12; sigma21 sigma22];
sigmainverse=inv(sigmaok);

times=sigmaok*sigmainverse;

Why is this?

Thanks

Answer 1

[John D'Errico]

Oh. So this is not an identity matrix?

simplify(sigmaok*sigmainverse)
ans =
[ 1, 0]
[ 0, 1]

That darn new math. Why must they keep changing things on me?

SOMETIMES, you need to use tools like simplify. Computers can be surprisingly silly at times, needing an extra hint, a little help.

[Lu Lu]

I know that but when you compute the second code you can see that you obtain NOT the identity, please give a try

[John D'Errico]

LOOK AT WHAT I DID!!!!!!! Do you not see that I used simplify on that second case?

THINK!!!!!!

I followed your code exactly. Executing what you did. Then at the very end, I added ONE extra thing, the simplify command.

Lesson: Computers sometimes need a hint. Apparently, sometimes people need more than a hint.

Think of it like this - is the number 2/2 equal to 1? The simplify function tells MATLAB to try just a bit harder to simplify a result. It asks, are you SURE that the answer is the mess you reported? Or can you do a bit better?

[Lu Lu]

I have tried

sigmaok=simplify([sigma11 sigma12; sigma21 sigma22]);
sigmainverse=simplify(inv(sigmaok));
sigmaok*sigmainverse

but

I have not the identity matrix, sorry but I do not know what to do to fix this

[Lu Lu]

Thank you very much, now I know