Consider a) f1=1, f2=sinx , f3=cosx
b) f1=1, f2=ex , f3=e2x
c)f1=e2x , f2=xe2x f3=x2e2x
in each part B={f1,f2,f3} is a basis for a subspace V of the vector space.
Find the matrix with respect to B of the differentiation operator D:V→V
two linear spaces S and S1 over F are isomorphic if and only if there is a one-to-one
correspondence x↔ x1 between the elements x \in S and x1 \in S1
such that if x ↔ x1 and y ↔ y1 then x+y ↔ x1+y1 and ax ↔ ax1
(y \in S , y1 \in S1, a \in F).
prove that two finite -dimensional spaces are...