1. Show that a plane through the origin in R is isomorphic to R2 2. Let T : R R3 where T'(u) is the reflection of u across the plane z 3y + z = 0. A. Find the matrix that represents this transformation. B. Find a basis for ker(7") and T(R3 )- C. Find rk(7T") and nullity (7). D. Is this transformation one to one? Justify your answer. E. Is this transformation onto? Justify your answer. F. )Based on your answers in part B and part C is this transformation an isomorphism. Justify your answer. G. (4 pts)Find all eigenvectors and their eigenvalues. H. (2 pts)Explain the results in Part (B) and (g)using geometry. 3.LetT : Py R where T'(p(x)) = p(1). Find a basis for the kernel and image of this transformation