Math 375 - 9/20

Question 1 • Why is span(∅)={0}? • 0 is the additive identity Question 2 • The basis of V={f∈P_n│f(0)+f^′ (0)=0}? • f(x)=a_0+a_1 x+a_2 x^2+…+a_n x^n • f(0)=a_0, f^′ (0)=a_1 • f(0)+f^′ (0)=0 • ⇒a_0=−a_1 • f(x)=a_1 (x−1)+a_2 x^2+…+a_n x^n • Therefore the basis of V is {x−1,x^2,…,xn}