Need help with this linear algebra

2. Let v be a nonzero vector in R\". A reector is a matrix R such that RX 2 x if a: 2'3 a scalar multiple of v, and Rx = x if v - x = 0. (1) Someone tells you that 'When applying a reector, the orthogonal complement of span(v) acts as a mirror.' Can you explain what that person meant? Draw a picture! (2) Show that R = 2P I , where P is projection matrix for projection onto the orthogonal complement of span(v). (If you haven't learned about projections onto arbitrary subspaces, then just consider the case n = 2). 3 Deduce from 2 that R = I iva. ( ) ( ) v-v (4) Deduce from {3) that RT = R and RTR =