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Subspaces, Basis, Dimension and Rank

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Please solve no. 12 and no. 30 in file scan005.jpg.

For problem 30; when claiming that a vector is in a space, demonstrate correctness by giving the coefficients.

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Subspaces, Basis, Dimension and Rank are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.