1. The problem statement, all variables and given/known data Let L: ℝn→ℝm be a linear transformation with matrix A ( with respect to the standard basis). Show that ker(L) is the orthogonal complement of the row space of A. 2. Relevant equations 3. The attempt at a solution The ker(L) is the subset of all vectors of V that map to 0. The orthogonal complement of W is the set of all vectors x with property that xw= 0. Would we use the dimension theorem: dim(ker(L)) = n - dim(range(L)) = n - dim(W) =dim(Wτ). Since Wτ is contained in ker(L). *Wτ is orthogonal complement.