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Question 1 (5 marks) Prove or disprove via counterexample the following statement: Let B = {c. 7, /} be a basis for FS. Then C = (8 - 7, 2 + 7, 27} is also a basis for F3. Question 2 (5 marks) a - 3b + 6c - 7d 5a + 10d Consider the subspace of R' which is defined as S = b - 2c+ 3d : a, b,c, deR 0 a) Determine a basis for S. Justify your answer. b) Determine dim(S). Question 3 (5 marks) Let B = be an ordered basis for R* such that = Determine 7 and B justify that B is a basis for R for your choice of v. Question 4 (5 marks) Let B be ordered bases for R?. Let 7 : R3 - R' be the linear transformation such that [a]s = [T(@)]c. Find T 2