1. The problem statement, all variables and given/known data Find the Eigenvalues of A= 4 0 1 -2 1 0 -2 0 1 Then find the eigenvectors corresponding to each of the eigenvalues. 2. Relevant equations 3. The attempt at a solution I found the Characteristic Polynomial of the matrix, computed the Eigenvalues which are 1,2,3. What I'm trying to get my head around is the concept of the eigenvectors. First of all I attempted to find the eigenvector(s) for λ=1. So I constructed the matrix (A-Iλ), row-reduced and got the matrix: 1 0 0 0 0 1 0 0 0 This matrix corresponds to the set of linear eqns (A-Iλ)x, and x must be non-zero. So normally I'd just read the solutions from this matrix and tell myself x1=0 and x3=0 I did this in maple and it gave me the value (0,1,0) as the eigenvector corresponding to λ=1, but x2 doesn't equal zero in any of these rows. Can someone explain this to me?