1. ## Orthogonal decompostion

ok so I am having a bit of difficulty expanding the answer to this question. since i can't type it out i found it online at this link: http://www.math.ust.hk/~macyfang/hw4.pdf

it's question #2 under section 6.3.

Now I know that I have to decompose v= v^ + z,

but is v^ = (v.u1/u1.u1)x u1? I got v^ to be (2, 4, 2, 2) and z to be (2, 1, -5, 1)

But i am wondering if this is correct, and if my calculation for v^ is correct..

I am thinking that if {u1.... u4} is an orthogonal basis, then the span of {u2, u3, u4} is orthogonal to span {u1}.

But for a 10 mark question, what have i left out??

2. Your solution seems right. Why do you think it's wrong?

Note that (2, 4, 2, 2) is indeed orthogonal to (2, 1, -5, 1).

3. my problem is that the working doesn't seem sufficient for the marks allotted for the question.. should there be more that I should add??

4. Originally Posted by Ife
my problem is that the working doesn't seem sufficient for the marks allotted for the question.. should there be more that I should add??
No, your solution is perfectly fine. (Don't worry about the marks alloted for a problem as long as you solve it correctly.)