For each of the following statements, choose whether it is True or False. Correct answers are worth one point each. (a) If A is a k x k matrix and A is not invertible, then > = 0 is an eigenvalue of A. [ Select ] (b) If B is a 4 x 4 real matrix, then B has at least one real eigenvalue. [ Select ] (c) The set 1 + '2 V = 12 + 3 : $1 , 12, 13 ER 1+ 2x2 + 23_ is a two-dimensional subspace of R3.|[ Select ] (d) If {01, 029. .., Un) is an orthonormal basis of R" and we R", then, for 1 S j s n, the coordinate of w with respect to , is given by the dot product w . aj. [ Select ] (e) If A is a k x k diagonalizable matrix then A is invertible. [ Select ] (f) If A is a 5 x 5 real matrix, then A has at least one real eigenvalue. [ Select ] (g) If A is a 5 x 6 real matrix, then A'A is diagonalizable. [ Select ] (h) The set {p(x) c R[x] : p(1) + p(2) = 0} is a (vector) subspace of the (vector) space of real polynomials, R[x]. [ Select ] (i) If A is a 7 x 11 real matrix, then A has at most 7 singular values. [ Select ] (i) The kernel of the linear map cty x - 2 2xty - z. is a two-dimensional subspace of R3.|[ Select ]