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Let P₂ (R) be the vector space of polynomials of degree less than or equal to 2 and P₁ (R) be the vector space of polyno
Posted: Tue Jul 12, 2022 11:59 am
by answerhappygod
- Let P R Be The Vector Space Of Polynomials Of Degree Less Than Or Equal To 2 And P R Be The Vector Space Of Polyno 1 (62.15 KiB) Viewed 32 times
Let P₂ (R) be the vector space of polynomials of degree less than or equal to 2 and P₁ (R) be the vector space of polynomials of degress less than or equal to 1. 1. Consider the linear transformation T: P₂(R) → P₁ (R) where T(ƒ) = f'. Find dim(N(T)) and dim (R(T)) and prove your claims. 2. Consider the ordered basis ß = {x² + 1, x² + x, x + 1} for P₂ (R) and the ordered basis y = {1, 2x} for P₁ (R). Compute [T]. [You do not need to show that B, y are bases.]