Question: Let T: R R be given by T - 2 Ty) (a) Show that T is a linear map by finding the matrix A

Let T: R R be given by T - 2 Ty) (a)

Let T: R R be given by T - 2 Ty) (a) Show that T is a linear map by finding the matrix A = [T] that represents it. (b) Find the eigenvalues (c) Check that the trace of A is the sum of these eigenvalues. (d) Find the eigenvectors of T. (e) Show that T is diagonalisable and write down the diagonal matrix D and the associated matrix P with P-AP = D. (f) Check that AP = PD. (g) Is T invertible?

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