1) This question concerns the linear transformation represented by a 3x3 matrix of real numbers.
With respect to the standard basis in both the domain and codomain.
(a) Determine the characteristic polynomial for A.
(b) Show that lambda = 1 is an eigenvalue and find the remaining eigenvalues of A.
(c) Determine all the corresponding eigenvectors and eigenspaces.
(d) Write down a matrix P and a diagonal matrix D such that (P^-1)AP=D
(e) Hence verify that (P^-1)AP=D by matrix multiplication.
Attachment:- BM05.zip