Problems Q1. Consider the ordered bases B = {r+z², 2+x², 1+x+2x²} and C= {1,1+x,1+x+x²} of P₂(F). (a) Compute the change of basis matrices CIB and BIC. (b) Let L: P₂(F) →

M2x2 (F) be the linear map defined by L(p(x)) Compute [L] and [L]e, where B and C are as in part (a) and & is the standard basis of M2x2 (F). (c) Use one of your matrices from part (b) to find bases for Ker(L) and Range(L). (d) Determine, with justification, whether L is (i) injective; (ii) surjective; (iii) an isomorphism. = [p(0) p'(0)]