1. Consider the Set S of all vectors in IR^5 perpendicular to the
following 2 vectors
(1 0 -1 2 -3) 
(2 1 0 0 -1)
You are told that S is a vector space:
a.	Calculate a basis of S.
b.	What is the dimension of S.
c.	Use Gram-Schmidt to calculate an orthogonal basis of S.
d.	Calculate the projection of the vector ( 3  1  -1  2  -4) on S

2. Let S be a subspace of IR5 described as follows 
	S = {(t1, t1 + t2, t1 + t2 + t3, t2 + t3, t3): t1, t2, t3 ? IR}
a.	Calculate a basis of S and write down its dimension
b.	Calculate the coordinates of (1  0  0  0  0) w.r.t the above basis
c.	Is the vector (1  1  2  1  1) in S?
d.	Project the vector u = (1  1  1  1  1) onto S
e.	Calculate the angle between u and projection of u