# Homework Help: Converting equations into vectores

1. Dec 30, 2011

### Jalo

1. The problem statement, all variables and given/known data

How do I convert a polinomial equation into a vector? Example:

x^2 + 3x + 1 How do I convert it into a vector like (x,y,z) (with as many variables as possible

2. Relevant equations

3. The attempt at a solution

The only thing I could remember was to isolate each x into a different vector, but I'm pretty sure I learned to do it in a better way at class, just don't remember it

x^2(1,0,0) + x(0,3,0 + (0,0,1)

Last edited by a moderator: Dec 30, 2011
2. Dec 30, 2011

### Staff: Mentor

I'm guessing that you are working with function spaces, which are similar to vector spaces. In a vector space, the coordinates of a given vector indicate a particular linear combination of basis vectors. For example, in R3, the standard basis is e1 = <1, 0, 0>, e2 = <0, 1, 0>, and e3 = <0, 0, 1>.

The vector <3, -1, 2> = 3e1 + (-1)e2 + 2e3.

In the function space of polynomials of degree 2 or less (P2), one basis is the set of functions {1, x, x2}. You can represent any polynomial of degree two or less as a linear combination of these basis functions.