An affine subspace of R" is a translation of a linear subspace, that is, any set of the form xo + U where to E R and UC R" is a linear subspace. The dimension of an affine subspace is the dimension of the linear subspace of which it is a translation. Show that WC R" is a k-dimensional affine subspace if and only if there are affinely independent vectors xo, ..., xk ER such that W = aff{xo,...,xk}.