All vectors and subspaces are in Rn Check the true statement

All vectors and subspaces are in Rn. Check the true statements below:

All vectors and subspaces are in R^n|. Check the true statements below: 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|. If z| is orthogonal to u_1| and u_2| and if W = Span{u_1, u_2}|, then z| must be in W. For each y| and each subspace W|, the vector y - proj_w(y)| is orthogonal to W|. If y| is in a subspace W|, then the orthogonal projection of y| onto W| is y| itself. The orthogonal projection y| of y| onto a subspace W| can sometimes depend on the orthogonal basis for W| used to compute y|.

Solution

A,B,C,D true

E is not true. The orthogonal projection does not depend on the basis.