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Suppose that {v1, v2, u} and {v1, v2, w}, are both bases for some subspace V...

Suppose that {v1, v2, u} and {v1, v2, w}, are both bases for some subspace V ⊆ R n .

(a) Demonstrate with an example that it is possible for {u, w} to be linearly independent.

(b) Assuming now that {u, w} is linearly independent, decide whether {v1, u, w} is necessarily a basis for V , giving justification for your answer.

For both parts it isn’t sufficient just to give answers, you must give convincing arguments, making appropriate use of mathematical notation and terminology to support your answers. In particular if you claim something is or isn’t linearly independent, or a basis, you must show it using either the definition or results from class, unsupported claims will not be accepted, you will be marked on how well you make your case.

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