Long Answer Questions. Complete the following questions while justifying your answers. Correct solutions without justication will not receive full marks. 1. [8 points] For each of the following statements indicate whether it is (always) true or (possibly) false, in the designated box 0 If you indicate that the statement is (possibly) false, you must provide a numerical example. You may use an example using vectors, or matrices, or functions! 0 If you indicate that the statement is (always) true, you must clearly explain why and justify your answer. :12): f (at) for all a: E R} is a subspace of the vector space of (a) [29'6] X = {f f( = IE'R > R} under standard operations. functions FUR Answer (T/F) [ .5pt ]: Justication / Counter Example [1.5pt] : (d) [2pt] The set {3:2 1,LL'2 + 11:, 1 at} spans P2 = {a + bu: + C$2|a, 13,6 6 R}, the vector space of polynomials of degree at most 2. Answer (T/F) [0.5pt]: Justication/ Counter Example [1.5pt]