Answer
a. True
b. True
c. True
d. False
e. False
Work Step by Step
a. W and $W^\perp$ are orthogonal, so if a vector v is in both, $v\cdot v=0$, which means v is the 0 vector.
b. Each term in formula 2 for $\widehat{y}$ is an orthogonal projection of y onto a 1 dimensional subspace spanned by one of W's basis vectors.
c. The orthogonal projection is in W, so z1 must be the orthogonal projection.
d. The best approximation is given by the projection of y onto W.
e. This is only true for orthogonal matrices, which are square.
