Question: Q1: (12 marks) In R4, consider the set S 2 {V1, V2, V3, V4, V5} where V] : (1,1,2a1): v2 : (2' 01 2,1), v3

Q1: (12 marks) In R4, consider the set S 2 {V1, V2, V3, V4, V5} where V] : (1,1,2a1): v2 : (2' 01 2,1), v3 : (3,15492); v4 : (4a 2, 6, 0) and V5 = (5, 1, 4, 1). You are given that RREF of the matrix A = [v1 V2 V3 V4 V5] is the matrix 10105/3'5 3:01108/3 00011/3 00000 (a) Find an ordered basis B of the subspace W = Span{S}. What is dim(W)? (b) For any vector V; from S that is not in B find [Vilg- Full marks will NOT be given without justification of your answer. (c) Which of the vectors a : (1,1,0, 1), b : (1,1, 1,0),c : (0, 0, 1, 1) is a basis for W1? Full marks will NOT be given without justification of your

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