Question

I know thats alot of information but if you could just answer exercises 7.19 and 7.20 at the bottom I would really appreciate it!!!! I WILL RATE!

Example 7.18 Consider a reflection across the line given in standard coordinates remember, ( must be a subspace, so must contain 0, the origin. Since the line isy=-3r, if we let z = 1, we get V--3, ald these are the coordinates of a basis wector for C. If we rotate this vector, say, by n/2, we.get a basis vector for the orthogonal complement of (, the line perpendicular by-C) Le. rotating every vector in f by /2 These two vectors form a basis transparent, from its definition (bi. ba) for R2 in which the action of R is Re(bi) b so that Re has a simple 8-representation, whichi Sollows from the above equations, 0 -1 Let us find its standard representation: using Proposition 6.18 1 0 # (-3-1) (0-1 103 1

Answer 1

5 19) The ne v 1 5 3-4