Question: Linear algebra question. Let u, v, W be (fixed, but unknown) vectors in IR and let A be an n x n matrix (fixed, but

Linear algebra question.

Let u, v, W be (fixed, but unknown) vectors in IR" and let A be an n x n matrix (fixed, but unknown). (a) (3 marks) Prove the following statement: If u, v, W are linearly independent and A is invertible, then Au, AV, AW are linearly independent. (b) (3 marks) Give a counterexample to show that the following statement is false: If I], V, W are linearly independent and A is nonzero, then Au, AV, AW are linearly independent. Hint: A counterexample should consist of a specific matrix A and specific vectors u, v, W (so you should write down all their components) so that 11, V, W are linearly independent, A is nonzero, but Au, AV, AW are linearly dependent

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