How to come up with eigenvectors? See more below.

Question

Hey, I was reviewing solving systems of differential equations and getting different answers from the textbook. When I solve the equations to get the values in the eigenvector, I am getting different values than in the textbook. If those values in the eigenvector work in the equations I get, I should be good right? The equations I am talking about are coming from the A-(eigenvalue)I, but using the eigenvalues, not lambda. Thanks for the help!

Answer 1

To find eigenvalues of a matrix A you need firstly to find the determinant of (A-xI). It will be a polynomial. Then equate this polynomial with 0 and find its roots. The roots will be the eigenvalues of A.

For eigenvectors of each eigenvalue x, you have to solve the system of linear equations (A-xI)v=0. Here you will find v, which will be your eigenvector of the corresponding eigenvalue x