Let S = {51,52,53,54} = {(4, 3,8, 5, 5), (5,7, 3,6,5), (3,4, 4,4,0), (6,5, 10,7, 3) . Denote W = Span(8). Now you are given 4 5 3 6 1 0 O 7/5 3 7 4 5 we), 0 1 0 4/5 A: 8 3 1 10 > 0 0 1 6/5 5 6 4 7 0 0 0 0 5 5 0 3 0 0 O 0 4 3 8 5 5 1 0 5 0 4 5 7 3 6 5 \"Pref 0 1 4 0 3 B: +-+ 3 4 1 4 0 0 0 0 1 6 6 5 10 7 3 0 0 0 0 0 Here are the questions. Make sure you explain your answer with some key words such as leading one's, non-zero rows. You do not need to do any calculation on nding the rref; however, you must state your reason of choosing one of the matrices above with the rref: a) Use matrix A and the rref to nd a basis of W. (You must quote the theorem and the whole statement of the theorem from our textbook). b) Use matrix B and the rref to nd another basis of W. (You must quote the theorem and the whole statement of the theorem from our textbook). c) Use the matrices and the rref to nd a basis of Wi. (You must explain your reasoning before doing the calculation)