11. Consider (A) =
(a) Find the eigenvalue and corresponding eigenvectors of A.
(b) Determine matrices B and C such that B A C is diagonal.
(c) Show the eigenvectors of (A) are linearly independent.
(d) Represent the vector < 1,1> in terms of the eigenvectors of A.
12. Let, γi and γj be distinct eigenvalues of A with corresponding eigenvectors ei and ej show that ei and ej are linearly independent.
13. Consider the stochastic matrix
(i) Find the eigenvalues of P.
(ii) If A = , find A^-1
Shown that (A^-1) (P) (A) = Diagonal and give the elements of it.
(iii) What are the eigenvectors of P?