(1 1) Let A, B E Mnxn (R) such that A is real symmetric with TAT > O,TER - 0} and B is skew symmetric matrix. (a) Show that det( A + B) + 0. (b) show A is invertible and A- is symmetric.(c) Show that A- has the property (d) Let V be a real vector space of all real sequences dif 1 = 90 = (a1, ...). Let U be a subspace of V defined by U = {aii-1 ( Van+2 = 2an+1 + 3an, n = 1, 2, ...}. Let T be the linear transformation from U to U defined by T((a1, a2, ...)) = (a2, a3, ...). Find any one of its eigenvalues and it's corresponding eigenvector of T