# 204PS52008 - Econ 204, Summer/Fall 2008 Problem Set 5 Due...

This preview shows pages 1–2. Sign up to view the full content.

Econ 204, Summer/Fall 2008 Problem Set 5 Due in Lecture Friday, August 15 1. In the following cases, show that matrices A and B have the same characteristic polynomials and hence the same eigenvalues. (a) B = A > , the transpose of A . (b) A and B are similar matrices. 2. Show that if an invertible matrix A is diagonalizable, then A 1 is diagonalizable. 3. Identify which of the following matrices can be diagonalized and provide the diagonalization. If you claim that a diagonalization does not exist, prove it: (a) 21 23 (b) 3 1 03 (c) 41 1 24 1 4 30 (d) 32 1 14 1 12 1 4. Consider the following quadratic forms: f ( x,y )=6 x 2 +4 xy +3 y 2 ,g ( xy Answer the following questions for each of these forms: (a) Find a symmetric matrix M such that the form equals ( xy ) M ( x y ) . (b) Find the eigenvalues of the form. (c) Find an orthonormal basis of eigenvectors.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 08/01/2008 for the course ECON 204 taught by Professor Anderson during the Fall '08 term at University of California, Berkeley.

### Page1 / 2

204PS52008 - Econ 204, Summer/Fall 2008 Problem Set 5 Due...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online