# Answer to Question #18529 in Linear Algebra for katie

Question #18529

Suppose that {v1.....Vn} is a basis for the vector space V. Given any vector v element of V, we can express v as a linear combination v = X1V1+.....+XnVn. The uniqueness of this expression means that mapping v to the n-tuple of coefficients (X1...Xn) defines a function O: V - R^n. Prove that this function is a bijection.

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