University of Wisconsin-Madison Mathematics Department

Math 340 Elementary Matrix and Linear Algebra Lecturer: Arun Ram

Fall 2007

Homework 10: Due November 14, 2007

1. Define eigenvector and eigenvalue of a linear transformation.
   
   
2. Define eigenvector, eigenvalue, and characteristic polynomial of a matrix.
   
   
3. Define λ-eigenspace and show that the λ-eigenspace is a subspace.
   
   
4. Show that if v₁, v₂, v₃ are eigenvectors with different eigenvalues then v₁, v₂, v₃ are linearly independent.
   
   
5. Do problems 5, 7, 10, 15, 19, 20 on page 451.
   
   
6. Do problems 10, 11 on page 461.