Suppose V is a finitedimensional vector space Define the dim

Suppose V is a finite-dimensional vector space. Define the dimension of V. (b) Recall that W = {p(t) P_2 | p(0) = 0}, i.e. the set of polynomials p(t) in P_2 such that p(0) = 0, is a subspace of P_2. Using your definition, find the dimension of W.

Solution

a) Dimension : Number of elements in the basis is called dimension of a vector space.

b) The basis for vector space of second degree polynomial with p(0)=0 is given by {x, x²}.

   Number of elemenents in the basis is two. Hence, the dimension is 2.