Please help with this linear algebra.

0 1. Consider the nonsymmetric matrix A = 3 (a) Calculate the eigenvalues of A and their corresponding eigenvectors. (b) Diagonalize A. i.e., find a nonsingular matrix S and a diagonal matrix A such that A = SAS-1. (c) Compute A 1000. (d) Is A orthogonally diagonalize A? i.e., does there exist an orthogonal matrix Q and a diagonal matrix A such that A = QAQT? 2. Consider the symmetric matrix A = Co (a) Calculate the eigenvalues of A and their corresponding eigenvectors. (b) Orthogonally diagonalize A. i.e., find an orthogonal matrix Q and a diagonal matrix A such that A = QAQT. (c) Compute A 1000 2 3. Consider the symmetric matrix A = (a) Knowing that the eigenvalues of A are A1 = 7, 12 = 13 = 1, find linearly independent eigenvectors el, x2 and 23 corresponding to these eigenvalues. (b) Orthogonally diagonalize A