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Definition: Let a_1, a_2, ..., a_n be scalars not all equal to 0. Then the set S consisting of all vectors X=[x_1; x_2; ... ; x_n] in R^n such that a_1x_1+a_2x_2+...+a_nx_n=c for c a constant is a subspace of R^n called a hyperplane. More generally, a hyperplane is any codimension-1 vector subspace of a vector space. Equivalently, a hyperplane V in a vector space W is any subspace such that W/V is one-dimensional. Equivalently, a hyperplane is the linear transformation kernel of any nonzero linear map from the vector space to the underlying field.