Consider the vector space R4 under usual addition and scalar multiplication. a) Determine whether the set S = {(2b − 3c, b, c, b - 5c): b, c are real numbers} forms a subspace in R4. b) Determine whether the set S = {(1,2,3,0),(-1, 1,8,1), (2,0, 1, 4), (1, 0, 8,1),(0,0,0,2)} forms a linearly independent set in Rª. Which vector(s) must be deleted so that the set is linearly independent. c) Determine whether the set S = {(1,−1,8, 5), (−2,0, 1, 0), (1, 1,0,0)} spans Rª. Which vector(s) must be added so that the set spans R¹. d) Find the dimension of the subspace spanned by the vectors (1,-1,0, 5), (2, 0,-1,3), (0, 2,-1,-7), (3, 1, -2, 1), (0, 4, 3,-1)}.

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