Let V be an n-dimensional vector space over F and B = {b₁,b2,...,b} be a linearly independent set of vectors in V where n > k. Suppose W = span(B). Prove that every vector a E V can be expressed as α = α₁ + α₂ where a ₁ EW and a 2 W. Show that a ₁ is unique but a 2 is not unique.

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