Question

Let p5 be the set of polynomials of degree 5 at most. Find the dimension of p5. Find two bases for p5 that have no vectors in common. Prove that your choices are bases.

Answer 1

P5 is generated by the usual basis 1,x,x^2,.. x^6 so it has dimension 6.

Answer 2

why is x^6 in the basis? i think that should be{1, x, x^2, x^3, x^4, x^5} n dim(P5) =6. well, i didn't get this_"Find two bases for p5 that have no vectors in common". if v1,...,vn and w1,...wm are bases for P5,then m=n. so what are the actually 2 bases for P5??? can i say v1,...,v5 and w1,...,w5 ???