Please show work and explain everything, thank you!
Suppose T is a linear transformation from a vector space V into a vector space V (T: V rightaarrow V). A vector u is called a fixed point of the transformation T if T(u) = u. a) Show that the set of all fixed points of Ta subspace of V. b) Let G: R^2 rightarrow R^2 be given by G(x, y) = (x, 5y). Then clearly G(2, 0) = (2, 0). Find the set of all fixed points of G. What is the dimension of the subspace formed by all the fixed points of G?
