Problem 4: Consider the set of polynomials {2+ t, 1 – 5t}. Let p¡(t) = 2 + t and P2(t) = 1 – 5t. Let B = {2+1, 1 – 5t}. (a) Show that the set B is a basis for P1. Show your work (define a basis if you...

Extracted text: Problem 4: Consider the set of polynomials {2+ t, 1 – 5t}. Let p¡(t) = 2 + t and P2(t) = 1 – 5t. Let B = {2+1, 1 – 5t}. (a) Show that the set B is a basis for P1. Show your work (define a basis if you use a coordinate mapping). (b) If [v (1)], find v(t). B (c) Find [1- 51 (d) Find -2+ 43t] B (e) Find 0 (t) where 0 (t) = 0 + Ot. B