Please show detailed work on each part

9. (14 points total) Let W = Span(S), Where S = {if$51, W2, 17153, 17154, 1755} C R5, and these are assembled in the columns of a matrix A. You are given that: 35015 10504 56726 01300 A= 1 3413 hasrrefR= 00017 _121~13 00000 24211 00000 45535 0000\" Li 351124 100222 563245 010%0i andAT= 07 412 5 withn'efR'= __5_ L __5_ 0016 2 3 121113 563315 000000 000 0 0 0 Think carefully about rows versus columns before answering the following: a. b. c. d. For '_I. Find a basis for Wwith integer coordinates using the information in R. Find a basis for Wwith integer coordinates using the information in R\". Express ii; = (0, 7,4, 1,2,5 ) in terms of your basis in (a). Express firs = (5,6,3, 3, l, 5 ) in terms ofyour basis in (b). Is the set S = {fir}, 17132, $3,324, 17155} dependent or independent? Explain your answer. Find a basis for W4 with integer coordinates. Explain how you got your answer in part (f), and how you chose which rref to use. Verify in writing that the rst vector in your answer to (f) is orthogonal to 17:4. State dim( W) and dim( Wi ). State the Dimension Theorem in general, and verify it for this W. Is { $2, {53, {is} also a basis for W? Explain your answer. Is { 17131 , 554, 555} also a basis for W? Explain your