Let p2 denote the vector space of all polynomials with degree less than or equal to 2. (a) show that b = {1 + x + x 2 , 1 + 2x − x 2 , 1 − 2x − x 2} is a basis for p2. (b) find the coord

The answer is in the the attachment

Step-by-step explanation:

The question you posted was incomplete but i believe below is the complete question;

Let P2 denote the vector space of all polynomials with degree less than or equal to 2. (

a) Show that B = {1 + x + x 2 , 1 + 2x − x 2 , 1 − 2x − x 2} is a basis for P2.

(b) Find the coordinate vector of p(x) = 1 + 2x + 3x 2 relative to the basis B

The answer is explained in the attachments.