1. Show that the operator L: R R defined by L((x, x)) = (2x1 + x2, x + x2) is linear. 2. Find the matrix representative of the linear operator L from Problem 1 with respect to the standard basis on both the domain and codomain. 3. Show that E = {(1,0), (1, 1)} constitutes an (ordered) basis of R2. 4. Find the matrix representative of the linear operator L from Problem 1 with respect to the basis E on both the domain and codomain.