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

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Let P2 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 (32.1 KiB) Viewed 19 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(f) = f'. Find dim (N(T)) and dim (R(T)) and prove your claims. 2. Consider the ordered basis B = {²+1, x² + x,x+1} for P₂ (R) and the ordered basis 7= {1, 2x} for P₁ (R). Compute [T]. - You do not need to show that B, y are bases.]