The vectors a1= (1, ,1 0) and a2= (1, 1, 1) span a plan in R3. Find a projection matrix P onto the plane, and find a nonzero vector b that is projected to zero.
I know a projection matrix is found with the formula A(A^tA)^-1A^t, but I don't really understand what the question is asking.
I've come up with P=[ (.5, .5, 0), .5, .5, 0), (0, 0, 1] and b = [1, -1, 0]. Does this look OK?