Please briefly explain the reasoning for each one. Thank you!

(1 point) All vectors and subspaces are in IR". Check the true statements below: BA. The closest vector to 3-; in a subspace W is given by the vector 3-; projWG). C] B. If E is orthogonal to {1 and 172 and if W=span(fi1 , :72), then 2 must be in Wi. C] C. If a matrix A is such that AT = A then the perpendicular complement of the kernel of A is the image of A. C] D. If W is a subspace and if a is in both W and Wi, then {7 must be the zero vector. C] E. The orthogonal projection 55 of 5; onto a subspace W can sometimes depend on the matrix used to compute 3.5. C] F. The columns of a matrix A are perpendicular to the rows of AT. C] G. If 3-; = 21 + 22, where Z] is in a subspace W and 22 is in Wi, then 51 must be the orthogonal projection of 3'; onto W. C] H. If 3-; is in a subspace W, then the orthogonal projection of J7 onto W is 37 itself. D, I. For each 5; and each subspace W, the vector 37 prot/()7) is orthogonal to W