Consider a nonsymmetric real matrix A which has the Schur decomposition A = QRAH where Q is unitary, and R is upper trian- gular. (a) Show that q which is the first column of Q is an eigenvector of A. Are the other columns eigenvectors? (b) Find a Schur decomposition of the matrix A = A -oggf. (c) What are the eigenvalues of A? (d) Assume that the eigenvalues of A are such that A1 A2 A3| > |A4|>... |n| where for simplicity it is assumed that the eigenvalues are all real. Suppose you use the power method and have computed the eigenpair A and u. Please propose a method for computing the next eigenvalue A2 by the power method applied to a certain matrix.