Question: All vectors and subspaces are in R ⁿ . Check the true statements below:

_ A. The orthogonal projection y-hat of y onto a subspace W can sometimes depend on the orthogonal basis for W used to compute y-hat.

_ B. If the columns of an n x p matrix U are orthonormal, then UU ^T y is the orthogonal projection of y onto the column space of U.

_ C. For each y and each subspace W, the vector y - proj _W (y) is orthogonal to W.

_ D. If z is orthogonal to u 1 and u 2 and if W = Span{ u 1, u 2}, then z must be in W┴

_ E. If y is in a subspace W, then the orthogonal projection of y onto W is y itself.

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