All vectors and subspaces are in r^n.

check the true statements below:

a. for each y and each subspace w, the vector y - proj_w (y) is orthogonal to w.

b. if z is orthogonal to u_1 and u_2 and if w = span{u_1, u_2}. then z must be in w.

c. the orthogonal projection y of y onto a subspace w can sometimes depend on the orthogonal basis for w used to compute y.

d. if y is in a subspace w, then the orthogonal projection of y onto w is y itself.

e. if the columns of an n times p matrix u are orthonormal, then uu^t y is the orthogonal projection of y onto the column space of u