lark each of the following (1)-(8) True (T) or False (F). You need not give a full proof but provide a brief justification, in a few sentences if possible. (Correct with justification - 4 pts, Correct but no or wrong justification 2 pts, Incorrect answer 0 pt.) (D) (T) IW, W% are subspaces of a vector space V then the union WiU W is a subspace of V. (2) ( ) The function T : M,xn(C) M(C) defined by T(A) = A, is linear over C. (3) ( ) Let V be a finite dimensional vector space over R Write V. for its dual space. If T : V, R is a linear functional on V' then there exists an element r V such that TU) f(x) for every feV (4) () Let A, B E M(R). If rank(A) k(B) then there exist invertible matrices P:Q e Mnxn(R) such that B-PAQ (5) Let A e MxR). If det(4) -0 then A 0 for some positive integer m (6) (F) The matrices (29 and 0.3) are unitarily equivalent. (Exery arthosonal operator on a finite dimensional real inner procduct space is disgonalizable. (8) ( ) Suppose that T" be a linear operator on a finite dimensional complex inner product space Then every eigenvalue of T +T is a real number