| # Dimension of an affine subspace The set in defined by the linear equations is an affine subspace of dimension . The corresponding linear subspace is defined by the linear equations obtained from the above by setting the constant terms to zero: We can solve for and get , . We obtain a representation of the linear subspace as the set of vectors that have the form for some scalar . Hence the linear subspace is the span of the vector , and is of dimension . We obtain a representation of the original affine set by finding a particular solution , by setting say and solving for . We obtain The affine subspace is thus the line , where are defined above.