Exercise 3.4.1

Find a Householder reflector P such that

P[296]=[1100].


z = [2,9,-6]; 

FNC.norm(z)
# 11.0

This is of the form that we can apply Theorem 3.4.2.

e1 = [1,0,0];

w = FNC.norm(z)*e1 - z;
v = w/FNC.norm(w);

P =  I - 2*v*v';

# verify
P*z

#3-element Vector{Float64}:
# 11.0
# -8.881784197001252e-16
#  8.881784197001252e-16