Find a basis for the subspace S in R⁴ spanned by all solutions of x₁​+2x₂​+3x₃​−x₄​=0. Find a basis for the orthogonal complement of S. Find b₁​​ in S and b₂​ in the orthogonal complement of S so that b₁​​+b2₂=b=(1,1,2,4).