# Week8 - v satisfying the equation A h-2 I v = Row reducing the augmented matrix we ﬁnd 1 4 3 0 3 h-4 3 h-4 0 8-4 h 8-4 h which row reduces to 1 4

This preview shows pages 1–5. Sign up to view the full content.

Assignment 8 Applied Linear Algebra Math 232(Fall 2008) Additional question: Show that h - 2 is an eigenvalue of the matrix A = h - 1 4 3 2 - h 2 2 h - 2 0 0 . Find an eigenvector corresponding to this eigenvalue. A1. We must show that A - ( h - 2) I is not invertible. Notice that A - ( h - 2) I = 1 4 3 2 - h 4 - h 2 h - 2 0 2 - h . We now compute the determinant using cofactor expansion along the third row to see that the determinant is ( h - 2) ± ± ± ± 4 3 4 - h 2 ± ± ± ± + (2 - h ) ± ± ± ± 1 4 2 - h 4 - h ± ± ± ± . Using the formula for the determinant of a 2 × 2 matrix, we see that the determinant is ( h - 2)(8 - 12 + 3 h ) - ( h - 2)(4 - h - 8 + 4 h ) = ( h - 2)(3 h - 4) - ( h - 2)(3 h - 4) = 0 Thus the determinant is zero and so h - 2 is an eigenvalue of A . To ﬁnd a corresponding eigenvector, we wish to ﬁnd a non-trivial vector

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

View Full Document

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.

Unformatted text preview: v satisfying the equation ( A-( h-2) I ) v = . Row reducing the augmented matrix we ﬁnd 1 4 3 0 3 h-4 3 h-4 0 8-4 h 8-4 h which row reduces to 1 4 3 0 1 1 0 0 0 . 1 The solution to this system consists of all vectors of the form t 1-1 1 where t is a free variable. Thus 1-1 1 is an eigenvector corresponding to the eigenvalue h-2. 2 Assignment 8 Applied Linear Algebra Math 232 (Fall 2008) Section 5.1 Section 5.2 Section 5.3...
View Full Document

## This note was uploaded on 06/14/2011 for the course MATH 232 taught by Professor Russel during the Fall '10 term at Simon Fraser.

### Page1 / 5

Week8 - v satisfying the equation A h-2 I v = Row reducing the augmented matrix we ﬁnd 1 4 3 0 3 h-4 3 h-4 0 8-4 h 8-4 h which row reduces to 1 4

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online