Hi, I need help with my Mathematics Linear Algebra. I will upvote!! Problem 1. (a) Prove that (.,:) is an inner product on Rn if and only if there exists a symmetric matrix A with strictly positive eigenvalues such that (x,y) = xt Ay for all x,y e Rn What is A when the inner product over R" is (x,y) = x - y, the usual dot product of the vectors x and y? (b) Let A e Mnxn(C), we say that M is self-adjoint when M* = M. Prove that (.,: is an inner product on Cn if and only if there exists a self-adjoint matrix A with strictly positive eigenvalues such that (x,y) = xt Ay for all x,y E Cn