6. (5 points) True/ false. Give a brief explanation/ counterexample for each part. (i) If v 6 R\" is an eigenvector for A and B , then u is an eigenvector for AB. (ii) If A, ,u 6 (C are eigenvalues of A, B respectively, then All is an eigenvalue for AB. (iii) If /\\ E (C is an eigenvalue for A, and c E (C, then (A + c)2 is an eigenvalue for A2 + 2cA + C21. (iv) If A E R\" is a symmetric matrix with an eigenvalue with algebraic multiplicity 2, then V?) 6 1R", {1),AU, . . . , fin11)} is linearly dependent. (v) If A = AT = PDP'I, where A 6 IR.\" and D is diagonal, then P is orthogonal