Question

Vectors

(1 point) All vectors and subspaces are in R^n

Check the true statements below:

\text { A. In the Orthogonal Decomposnion Theorem, each lerm } \hat{y}=\frac{y \cdot u_{1}}{u_{1} \cdot u_{1}} u_{1}+\ldots+\frac{y \cdot u_{p}}{u_{p} \cdot u_{p}} u_{p} \text { is itselt an orthogonal projection of } y \text { onto a subspace of } W

\text { B. If an } n \times \text { p matrix } U \text { has orthonormal columns. then } U U^{T} x=x \text { for all } x \text { in } R^{n}

C. The best approximation to y by elements of a subspace W is given by the vector y- projw (y).

D. If y = 21 + z, where z, is in a subspace W and z2 is in W^1, then 2, must be the orthogonal projection of y onto W.

E. Ir W is a subspace of R^n and if v is in both W and W, then v must be the zero vector.