Problem 1: A matrix is symmetric if A = AT while a matrix is skew-symmetric if A = -AT. Consider specifically a square marix A. a) Show that S (A +

AT) is symmetric. = b) Show that K(A-AT) is skew-symmetric. c) Noting that A = S + K, write the following matrix A as the sum of a symmetric and a skew-symmetric matrix. A = 16 15 14 13 12 11 10 9 8 7 6 5 3 2 1 00 4