Problem 3. Show that {1+x,x+x², x² + x³, x³} is a basis of the space P3.
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- For Problem #12, how do I prove that the set is a basis for V? I think that infinity is the basis, but I'm not sure. This is a Linear Algebra type of question. Here is a picture.Following question is from a linear algebra course, We consider a second basis of V, C = {1 + X, X + X2, X2 + X3, X3}. (You don't have to prove that C is indeed a basis of V). Show what the image under fC is of:• the four basic elements: Q1(X) = 1 + X, Q2(X) = X + X2, Q3(X) = X2 +X3 and Q4(X) = X3 • P(X) = 2 + 6X + 3X2 + 4X3.show that {x-2x^2,3x+1,-1} is a basis for P3}