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 .

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.