All vectors and subspaces are in R". Check the true statements below: A. If W is a subspace of R" and if v is in both W and W, then v must be the zero vector. B. In the Orthogonal Decomposition Theorem, each term y=y.u1/u1.u1 u1 +.... + y.up/up.up up is itself an orthogonal projection of y onto a subspace of W.
C. If y = 21 + 22, where 2₁ is in a subspace W and z2 is in W, then 2₁ must be the orthogonal projection of Y onto W. D. The best approximation to y by elements of a subspace W is given by the vector y – projw(y). E. If an n x p matrix U has orthonormal columns, then UUT x = x for all x in R".