For this section state whether the following statements are True or False. Pro- vide complete justifications for your choice. Each question is 10 points. 11) Let T : R4 - R3 be a linear transformation. Then the dimension of kernel of T is atleast 1. 12) Let u be a vector in R2 such that u is orthogonal to en + ez and e1 - ez, then u has to be the zero vector. Here e, and ez are elements of the standard basis in 2. 13) Let S be a set of 20 vectors in R20, then S forms a basis of R20. 14) Let vi, v2, v3, V4, Us are vectors in Ro such that the intersection of the sub- spaces Span (v1, U2, v3) and Span(14, 15) is the zero vector. Then (v1, v2, v3, U4, 15) is linearly independent. 15) Let A be a 3 x 3 matrix such that v1 and v2 are vectors which satisfy Av1 = b and Av2 = b, then 2v1 - 302 6 Null(A)