Let U be the subspace of R^4 with the basis

(1; 0; 1; 0); (0; 1; 1; 0); (0; 0; 1; 1):

Use the Gram-Schmidt process to nd an orthonormal basis for U.

Note - R4 is that strange looking R with a double | at the left of it.

Right, so I know the first few steps for this question.

Take y1 = (1; 0; 1; 0); y2 = (0; 1; 1; 0); y3 = (0; 0; 1; 1):

Put x1 = y1 = (1; 0; 1; 0). Simples.

The next formula I think is something like x2 = y2-((y2*x1)/(x1*x1))*x1

But I keep getting out -1/2(1,0,1,0), and to top it off there's another formula for the next bit that I have no idea about. The lecturer has already said that the answer should be 1/2(1,0,1,0) [or 1/2x1 if you prefer.]

So, to clarify; i) How do you multiply two vectors together (eg (0,1,-1,0)*(1,0,1,0) like in the above example.) ii) What have I done wrong in the last part of the solution given? iii) What is the formula required for the next step?

Many thanks to those who can help me! This is going towards my resit paper in a few days by the way, so wish me luck.