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We may even think of certain sets of matrices as vector spaces (you can assume this is true without checking)

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We may even think of certain sets of matrices as vector spaces (you can assume this is true without checking). Consider the set of all 3 x 3 matrices. Give an example of a basis for this vector space, and briefly explain why your answer is a basis - you do not need to rigorously show that it is a basis. Hint: This vector space will need nine vectors in its basis).