6. (10 points) Is the set S = {(153), (0,1,2), (1,6,7), (1, -3,2)} a basis for the vector space R3? Briey explain your answer. 7. (to points) Let 3 = {(12.3) , (1,2,0), (0, 6,2)} and f = (1, -2,0). IfB is a basis for R3, nd [3:13. If B is not a basis, explain why it isn't. a. (no points) Given a = {(1.1.-1) . (1.1.0). (1. -1,o)l and B' = {(1.23) , (1,2,0), (0, 6,2)}. Find the transition matrix from B to B'. 1 Use your result to nd [55],: for [13 = [ 2 I. -1 9. (10 points) The matrix B has been obtained from a matrix A by row operations. 1 0 3 0 -4 1 3 0-4 102) 309011 001 000 5 0 15 0 20 Use the matrices to nd the following: a. The rank and the nullity of A. b. The rank and nullity of AT. c. A basis for the null space of A. d. A basis for the row space of A. c. A basis for the column space of A. 121'] OOHO lo. (10 points) Consider the matrix A = a. Is [3] in the column space of A? Justify your answer. b. Is [1 1 - 2] in the row space of A? Justify your answer. 0. Find any vector in the null space of A. Justify your