I guessed two additional vectors in order to complete the basis, (1, 2, 0) and (1, 0, 3), then I performed Gram-Schmidt to orthonormalize my basis. If my basis is X=(x1, x2, x3), I am confused because I have written in my notes to perform Gram-Schmidt on just x2 and x3, and not x1.

Anyways, I continued the problem as I have it in my notes. I calculated:

z1= [1/(square root 5)](1, 2, 0)

z2 = [1/(square root 245/25)](.8, -.4, 3)

Now I must find the inner product of (1, 0, 0) and z^i for i = 1,2... and this is the step I do not understand.

Next I have the Projection = Sum(inner product (1, 0, 0) , z^i))z^i.

Can someone walk me through the end of this problem? Thanks.