This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
**Unformatted text preview: **A , then Î» n is an eigenvalue of A n . How are the corresponding eigenvectors related? 1 2 5. Show that if A is invertible and ~v is an eigenvector of A , then ~v is also an eigenvector of A-1 . how are the corresponding eigenvalues related? 6. Find a matrix 2 Ã— 2 matrix A that has eigenvalues 2 and 3 with corresponding eigenvectors Â± 1 2 Â² , Â± 1 3 Â² respectively. 7. Is it true that every invertible matrix is diagonalizable? Justify your answer. 8. Let A = Â± 4-1-2 5 Â² . Calculate A 3 . Verify your answer by computing A 3 directly. 9. Let A = Â±-2 2-3 5 Â² . Calculate A 200 . 10. Let A = Â± 2 2-3-5 Â² . Calculate A 100 ....

View
Full
Document