2.39 Consider the vector space S = {u : u = Ax,x R*}, where A...

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2.39 Consider the vector space S = {u : u = Ax,x € R*}, where A is the 4 x 4 matrix given by [1 2 1 1 A = 1 0 2 2 4 3 1 3 -2 0 PROBLEMS 89 (a) Determine the dimension of S and find a basis. (b) Determine the dimension of the null space N(A) and find a basis for it. (c) Is the vector (3, 5, 2, 4)' in S? (d) Is the vector (1, 1, 1, 1)' in N(A)? 2.39 Consider the vector space S = {u : u = Ax,x € R*}, where A is the 4 x 4 matrix given by [1 2 1 1 A = 1 0 2 2 4 3 1 3 -2 0 PROBLEMS 89 (a) Determine the dimension of S and find a basis. (b) Determine the dimension of the null space N(A) and find a basis for it. (c) Is the vector (3, 5, 2, 4)' in S? (d) Is the vector (1, 1, 1, 1)' in N(A)?