Question: 1. Let u1, u2, u3, u4 ( R' and suppose that {u1, u2, u3, u4} is linearly independent. Answer each of the following questions by

1. Let u1, u2, u3, u4 ( R' and suppose that {u1, u2, u3, u4} is linearly independent. Answer each of the following questions by either giving a proof or a counterexample. (a) Does there exist us E R' such that {u1, u2, u3, u4, us} is linearly independent? (b) Do there exist us, us E R' such that {u1, (2, u3, u4, us, us} is linearly independent? (c) Do there exist us, us E R' such that {u1, u2, us, (4, us, us} is linearly independent and u1, . . ., us are all different

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