You can write the set of equations as
A is diagonalisable into the diagonal matrix through a transition matrix P such that
is transposed into
Since D is diagonal is easily solved.
Then is used to find and
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
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?