Right i have a rather large project to do and its split into 12 parts. This is the first part and im posting my answer to it. I one of those 'using the result of the previous part' projects so i figure i'd better get the first part right! Could someone please tell me if this is done right?

Let P denote the vector space of real polynomials and

the subspace polynomials of degree

. We define an inner product on P by

.

1. Apply the Gram-Schmidt procedure to

to construct an orthogonal basis of

. Normalize the basis vectors such that they take the value 1 when x = 1. (Im having a bit of trouble with the normalization bit...)

My solution so far... (shortened a bit cos its a lot to type!)

and

is the basis i am trying to find.

Let

_______________________

so

__________________________________

so

_______________________________________________

so

__________________________________________________ ___

so

SO!

basis is

If thats right how do you normalize it?