I need some help, I think in 1) I just have to show that they're lin.indepent and have trivial solutions a1=a2=0.
Let P3(R) denote the R-vector space of real polynomials
p = a + bX + cX2 , where a,b, c ∈ R, of deg. ≤ 2.
1) Argue that, p1 = 1 − X^2 , p2 = X − X^2 , spans S. Where, S = {p ∈ P3(R) | p(1) = 0}.
2) Argue that S can't be spanned by a single element.
3) Conclude that the dimensions of S equal 2.
Let P3(R) denote the R-vector space of real polynomials
p = a + bX + cX2 , where a,b, c ∈ R, of deg. ≤ 2.
1) Argue that, p1 = 1 − X^2 , p2 = X − X^2 , spans S. Where, S = {p ∈ P3(R) | p(1) = 0}.
2) Argue that S can't be spanned by a single element.
3) Conclude that the dimensions of S equal 2.
