please help me on this question All vectors and subspaces are in R^n. Check the

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please help me on this question

All vectors and subspaces are in R^n. Check the true statements below: If an n times p matrix U has orthonormal columns, then UU^T x = x for all x in R^n. The best approximation to y by elements of a subspace W is given by the vector y - proj_w(y). In the Orthogonal Decomposition Theorem, each term y = y middot u_1/u_1 middot u_1 u_1 + ... + y middot u_p/u_p middot u_p u_p is itself an orthogonal projection of y onto a subspace of W. If W is a subspace of R^n and if v is in both W and W^-1, then v must be the zero vector. If y = z_1 + z_2, where z_1 is in a subspace W and z_2 is in W^-1, then z_1 must be the orthogonal projection of y onto W.

Explanation / Answer

A. is False,This only holds true if U is a square matrix and not for every matrix.

B is False.projwy will give the best approximation.

C This is true.

D.This is true

E.This is true.

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