Explore BrainMass

Probs in Linear Algebra

1 3
11. Consider (A) =
2 1

(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, &#947;i and &#947;j be distinct eigenvalues of A with corresponding eigenvectors ei and ej show that ei and ej are linearly independent.

13. Consider the stochastic matrix

2/3 1/3
1/4 3/4

(i) Find the eigenvalues of P.

1 4
(ii) If A = , find A^-1
1 -3

Shown that (A^-1) (P) (A) = Diagonal and give the elements of it.
(iii) What are the eigenvectors of P?