• Oct 29th 2012, 02:23 PM
angelme
I don't know understand what is BASIS in vector. I try to read it on the book but still.. :(

I want to solve this question but I don't know how to begin with. Someone please help explain.

Finding a basis for the set of the function spanned by x2-1, x2+1, x, and x+1
• Oct 29th 2012, 08:41 PM
chiro
Hey angelme.

A basis is just a collect of vectors that describe the whole space you are dealing with. In geometry we usually write any three dimensional vector as V = ai + bj + ck where a,b,c are real numbers and i,j,k are vectors corresponding to the x,y,z axis in 3D geometry. They don't have to be these specific vectors but this is a common basis: as long you can construct any vector in the space using a linear combination of the basis vectors, then the basis vectors constitute a basis.

Instead of having a vector in <x,y,z> you have a polynomial in <x^2,x,1> where you have basis vectors x,y,z such that X = ax + by + cz describes all possible vectors X in your space.

Now you need to identify a basis for the polynomial and the first step is to think of the x^2 terms independent to x terms and x terms independent to constant terms: in fact all three will be independent from each other and then think of these as vectors <x,y,z> instead of <x^2,x,1>
• Oct 30th 2012, 08:01 AM
angelme
So the basis for the set of the function spanned by x^2 -1, x^2 +1, x, and x+1 is (x^2,x,1) simple as that ?
• Oct 30th 2012, 08:43 AM
Deveno