Let B={v_1...v_n} be some basis for R^n. Prove that if x is an element of R^n then x can be expressed as a linear combination of the basis vectors in a unique way. (i.e. if x=a_1v_1+...+a_nv_n and x=b_1v_1+...+b_nv_n then a_i=b_i for each i.)

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