Consider the following three vectors in R: V = (a) Show that = (V, V2, V3) is a basis for R. Consider the following four vectors in R4: = 1 --0--0---0--(-)) = 1 -(). -(-9). -0). 0 = V3 = 3 1 1 (b) Show that B = (U, U2, U3, U4) is a basis for R. A linear map T: R4 R is determined by: (d) Give a basis for the image of T. = (e) Give a basis for the kernel of T. T(u)= V, T(u) = 2v2, T(u3) = T(U4) = 0, (c) Give the standard matrix of T, i.e., in terms of the standard bases for R4 and R. = For all the points above, write full sentences explaining all the steps. 1 [4 Marks] [4 Marks] [9 Marks] [4 Marks] [4 Marks]