8 Which of the following sets form a basis for P2 a W 1 x

8. Which of the following sets form a basis for P2 :

(a) W = {1 ? x, 1 ? x + x 2 , 1 + x 2 , 1 ? x ? x 2}

(b) W = {1 ? x, x ? x 2 , 1 + x 2}

(c) W = {1 + x, 1 + x 2}

8. Which of the following sets form a basis for P2 (a) w = { 1-x, l-2+ r2, i + 12, 1-1-12} (b) w=(1-1, 1-12, + r*)

Solution

(a) W = {1 x, 1 x + x 2 , 1 + x 2 , 1 x x 2}

is the   form for the basis for P2