Answer to Question #18235 in Vector Calculus for katie

Question

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.