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Consider the subspace S = {[x, y, 2x + 3y] | x, y ∈ R} of...

Consider the subspace S = {[x, y, 2x + 3y] | x, y ∈ R} of R 3 . (a) Find a basis of S and dim (S). (b) Extend the basis of S in (a) to a basis of R 3 .

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