Let V be a subspace of R3[t] consisting of polynomials p with p(1) = 0. Let
b1 = t^2 -t
b2 = t^3 + t^2 + t - 3
b3 = 2t^3 - 5t^2 - 7t + 10
Determine if the set of vectors span and if they are linearly independent.
I'm not really sure what to do with the p(1) = 0. The text says to use the basis {t-1, t^2-1, t^3 -1} and then use the coordinates of the vectors in that basis. I'm not sure how to get that basis.
thanks!!