Question

Find a basis {p(x),q(x)} for the vector space f(x) € P3[x] where P3[x] is the vector space of polynomials in with degree less than 3. p(x) = ,q(x) = =

Answer 1

To find a basis for the vector space f'(1) = f(1), choose p(x) = 1 and q(x) = (x-1)+1.

Step-by-step explanation:

To find a basis for the vector space f(x) € P3[x] , we need to find two polynomials p(x) and q(x) that satisfy the given condition. In this case, p(x) and q(x) both need to have a derivative of 1 and evaluate to 1 at x = 1.

One possible basis for this vector space is p(x) = 1 and q(x) = (x-1)+1.

Both polynomials have a derivative of 1 and evaluate to 1 at x = 1. Therefore, the basis for the vector space is {p(x) = 1, q(x) = (x-1)+1}.