1. The problem statement, all variables and given/known data Find h in the matrix A such that the eigenspace for lambda=5 is two-dimensional. A= [5,-2,6,-1] [0,3,h,0] [0,0,5,4] [0,0,0,1] A-lambda*I(n) = [0,-2,6,-1] [0,-2,h,0] [0,0,0,4] [0,0,0,-4] 2. Relevant equations 3. The attempt at a solution I'm not really sure how to do this. Is there some relation between algebraic multiplicity and the eigenspace of a matrix that would help? I tried solving this by row operations to solve for the eigenvectors in the hope that I would be able to eliminate values of h that would have resulted in more or less than a 2 dimensional eigenspace, but it didn't work out. This is the matrix I got (keep in mind this is after applying the lambda value to the diagonals) A= [0,-2,6,-1] [0,0, h-6,1] [0,0,0,4] [0,0,0,0]. I'm pretty confused about this any help would be greatly appreciated. Thanks.