[Lewk]

I am wondering how to write q(x)= 2 + 3x + 4x²

in terms of the basis S={1+x, 2+x², x-x²}, without using 'observation'. I remember there was a matrix method.

Any help would be great

[jj193]

S is a basis you don't like
Can you write a more preferable basis in terms of S? i.e. 1,x, xx
This is a basis change...

[latentcorpse]

(Original post by Lewk)
I am wondering how to write q(x)= 2 + 3x + 4x²

in terms of the basis S={1+x, 2+x², x-x²}, without using 'observation'. I remember there was a matrix method.

Any help would be great

This is essentially a change from the basis to your new basis

Suppose , then you can set up three simultaneous equations:

and solve them

You should find that