Lin. Algebra: Is P2 a subspace of P3

[veege]

Homework Statement

Simple enough: Is P₂ a subspace of P₃?

Homework Equations

The Attempt at a Solution

I think it is. All P₂'s can be written in the form 0x^3 + ax^2 + bx + c. Then, it's easy to see that it's closed under scalar addition and multiplication.

Our professor mentioned that R₂ is NOT a subspace of R₃, so that's throwing me off here. Anyone?

 

[Mathnerdmo]

Your solution to the problem looks good (if a little short, and I think you mean "addition and scalar multiplication").

What is R₂ and R₃ here?

 

[veege]

thanks for the correction.

oops, I meant R^2 and R^3.
But I found a thread that helped me to understand this, here: https://www.physicsforums.com/showthread.php?t=129661