Hi, my friend asked for help with a question and I'm wondering if there's a better method than mine by the question wording.

We have the matrix

and have to find the eigen values and vectors which are

3 with

and

1 with

The next part is to solve the set of equations

using the eigenvalues and eigenvectors.

As this is of the matrix form I solve this by writing characteristic equations with the eigenvalues as the exponentials

and substituting into the above equations to get six equations in A,B,C,D,E and F thus leading to

which is right!

However, I haven't used the eigenvectors only the eigenvalues, is there another (better ? ) method that I should be using?

Thanks!