Let V be a p-dimensional subspace of R^n. We define the reflection in V operator reflV :
R^n -> R^n as reflV(x) = 2projV x - x.
(a) If V is a line in R^2, picture the effect of this operator on a vector in R^2.
(b) Show that reflV is a linear operator.
(c) Show that reflV is one-to-one, that is, if reflV (x) = 0 then x = 0.