Originally Posted by

**bugatti79** All,

Let V be the vector space of all polynomials of degree 3 at most. Is the set

$\displaystyle A=\left({x^3+2x+3, x^2+4x-1, x+5,2x}\right)$ linearly independent? Is A a basis for V

First of all i want to establish the difference between 'basis' and 'its dimension'. I am thinking they mean the same thing...ie, $\displaystyle {\mathbb{R}}^3$ is of dimension 3 because you need 3 linearly independant vectors to get to a point in 3D space. THis is the same as saying it has a basis involving 3 vectors.....correct me if im wrong...

Thanks