1. I.11 Linear Spaces

Condition: let \ (m- \) many polynomials \ (p \ in \ mathb {p} _ {n} \) with material coefficients that satisfy these conditions. To prove that \ (m \) is a linear subspace in \ (\ mathb {p} _ {n} \), find its basis and dimension. Add the basis \ (m \) to the basis of the entire space \ (\ mathb {p} _ {n} \). Find the matrix of the transition from the canonical base of the space \ (\ mathbb {p} _ {n} \) to the built basis. \ [n = 4, \ quad p (t) \ in m, \ quad p (-2) = p (3) = 0 \ text {. } \]