What is the basis and dimension of the subspace U of P2?

[Hockeystar]

Homework Statement

Find the basis and dimension of the following subspace U of P₂

p(x) \ni P₂ such that p(1) = p(2)

Homework Equations

The Attempt at a Solution

I know all quadratics are in the form ax² + bx + c

set p(2) = p(1)

4a + 2b + c = a + b + c
b = -3a

Therefore ax² -3a + c

Basis(U) = a(x²-3x) + c

Therefore dim(U) = 2

I'm just wondering if I have the correct answer or not. Going into linear algebra midterm tomorrow and prof never really went over polynomials but it's on the test.

 

[micromass]

I assume P2 is the space of all second degree polynomials (the notation P2 is not standard, so includi it next time ). Then your proof is correcT.

The basis for U is by the way \{x^2-3x,1\}. What you wrote down doesn't make much sense to me...

 

[Hockeystar]

Thanks for the reply. I just wanted clarification that I'm properly solving the problem. My format was off because I used subscript instead of superscript.