The subspace W of is given by the vectors:

u=(1,1,0,1)

v=(1,-1,1,0)

w=(1,-1,0,-1)

I need help calculating the projection of the vector x (1,1,1,1) in to the subspace.

I know I need to make all the vectors orthogonal and then i can use the following formula:

My question is can i use the first two vectors (that happen to be orthogonal) and just use Gram Schmidt on the last vector to make it orthogonal or do I have to use Gram-Schmidt on all the vectors?

I tried using Gram-schmidt on the third vector to get it orthogonal, this got me the following vector.

I put this vector in to the formula above and came up with the following projection:

Are my calculations correct?

/Maria