Suppose that an n x n matrix A is nondefective, b is an n-vector, and a* is so that * = A* + b. For a starting n-vector ro, consider the iterations *k+1= Axk+b, k=0,1,.... Define the error ek = xk - x*. (a) Show that ek+1 = = Akeo- (b) Show that ek →0 (the iteration converges) as k∞ for an arbitrary to if and only if p(A) <1, where p(A) is the spectral radius of A. [Hint: Can you express the initial error (eo=xo-*) as a linear combination of the eigenvectors of A? Why?]