how to solve solve matrix in Ax=b

Hello,

I have a system A=B(X^-1). Where A is nxm, B is nxm and X^-1 is mxm. All of them are complex and the matrix X is similar to below:

I want to save the equation in variable then solve it using "vpasolve" to find wanted unkwons.

[John D'Errico]

What d you want to compute? Is A known? Is B known? Is X known?

It seems you are telling us that X is an unknown 5x5 tridiagonal matrix of that form, with 13 unknown elements, and all you know is that X is tridiagonal?

If that is the case, then no, you cannot solve for X. You cannot use vpasolve to do so.

If A and B are known, then you can write this problem as effectively

X^-1 = inv(B)*A

then invert that result to find X. You would then have

X = inv(A)*B

If the resulting matrix X is tridiagonal then you have succeeded. In no respect do you ever need to use vpasolve. Simple linear algebra would succeed.

However, if the matrices A or B have less than full rank, then the above formula will fail. And we are not told anything about A or B.

Answer 1

[Basem Bazuhair]

A and B are not square matrix, so we can not find the inverse.

X is tridigonal matrix, and it has the below shape for 3x3 or 4x4.

I want to save the equation as below then solve it.

Syms XX [m,m]
Xinv = (det(XX)*adjoint(XX))
B(n,:)*Xinv(:,m) == A(n,m)