6. Eigenvalue estimates [2+2+2pts] Gerschgorin's second theorem states that if the union of k Gerschgorin discs is disjoint from the other n - k discs, it must contain exactly k

eigenvalues.Now let for some z E C. Here i is the imaginary unit. (a) Sketch the first two Gerschgorin discs for A. (b) Suppose we know that at least two of the three eigenvalues are equal. Using Gerschgorin's theorems, what can we conclude about the value of z? (Find the largest subset of C that you know z cannot be in) (c) Suppose we know that all eigenvalues are equal. What can we conclude about z?