so I actually have two separate questions which are homework bonuses for my numerical methods course. Unfortunately, because of the time of the semester, our TAs are not available so I don't have many resources for help so I'm turning to you all, who have helped me in the past!
The first question is:
Consider the matrix A = [{a, 1, 0}, {0, a, 0}, {0, 0, a}] where a is constant. Determine all the eigenvalues and associated eigenvectors.
As far as I'm aware, we never talked about eigenvalues of asymmetric matrices in class, so I am really at a loss here. We have mostly focused on the power rule, which as far as I can tell doesn't seem to work for this particularly problem (the values don't seem to converge?)
The next question is:
Reformulate the problem of finding a min or max for a function D(x1, x2) as a rootfinding problem for a system of two equations and two unknowns. We assume the function D(x1, x2) is differentiable with respect to both x1 and x2.
And this one I really.. don't even know where to start.
For either problem, any help would be hugely appreciated!