In Exercises 43-48, V is a nonzero finite-dimensional vector space, and the vectors listed belong to V. Mark each statement True or False (T/F). Justify each answer. (These questions are more difficult than those in Exercises 17-26.) 43. (T/F) If there exists a set {V₁, ..., Vp} that spans V, then dim V ≤ p. 44. (T/F) If there exists a linearly dependent set {V₁, ..., Vp} in V, then dim V ≤ p. 45. (T/F) If there exists a linearly independent set {V₁,..., Vp} in V, then dim V≥ p. 46. (T/F) If dim V = p, then there exists a spanning set of p + 1 vectors in V. 47. (T/F) If every set of p elements in V fails to span V, then dim V > p. 48. (T/F) If p≥ 2 and dim V = p, then every set of p - 1 nonzero vectors is linearly independent. 49. Justify the following equality: dim Row A+ nullity A = n, the number of columns of A 50. Justify the following equality: dim Row A+ nullity AT = m, the number of rows of A