Converting equations into vectores

[Jalo]

Homework Statement

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

Homework Equations

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)

Thanks ahead

 

[Mark44]

Homework Statement

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

Homework Equations

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)

Thanks ahead

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.