Consider the matrix A R"*" with distinct eigenvalues \\q,..., A, and eigenvectors vy,...,v,. Define the linear operator F : C"* C*" by F(X)=AXAT - X. (a) Find the eigenvalues and eigenvectors of F. (b) Under what conditions is F singular? 0 1 ( ~1 0 ( d) For the same matrix A, find bases for the range and nullspace of F. ) ) c) For A= [ ] find the rank and nullity of F. ) ) (e) Consider a matrix A whose eigenvalues satisfy |A\\i|