Find the matrix that projects a vector from R^4 onto the space spanned by

[1/2] [1/2]

[1/2] [1/2]

[1/2] [-1/2]

[-1/2] [1/2]

(the given vectors are orthonormal)

Let T: R^3R,

where T([v1 v2 v3]) = v1 -3(v2+v3).

Prove that T is a linear transformation.

Prove whether or not each set is a subspace of R^3:

a. S1: The set of vectors [x y z] where x=y

b. S2: The set of vectors [x y z] where x = yz