This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 20D Exam #2 25 November 2009 1. (15 points) Find all the eigenvalues (with multiplicity) and the eigenvector(s) associated with the largest eigenvalue for the following matrix.  6 3 6 2 1 2 4 2 4 Solution: det  6 3 6 2 1 2 4 2 4 = ( 6 )det 1 2 2 4  3det 2 2 4 4 + ( 6)det 2 1 4 2 = ( 6 )( (1 + )(4 ) + 4) 3(8 2  8) 6( 4 + 4 + 4 ) = ( 6 )( 4 3 + 2 + 4) + 6  24 = (( 6 )(  3) 18) = ( 18 3  2 18 ) = 2 (3 + ) . Thus the eigenvalues are 3, 0, and 0, with 0 being the largest. Now reducing the matrix associated with the eigenvalue 0, we get  6 3 6 2 1 2 4 2 4 2 1 2 Thus, two linearly independent eigenvectors associated with 0 are 1 1 1 2 . 2. (20 points) The matrix A has the eigenvalues 3 2 i , 1, and 2. The eigenvector are  1 4 2 i  1 2 , 2 3 , and  2 1 4 2 , respectively. Write down therespectively....
View
Full
Document
This note was uploaded on 01/26/2010 for the course MATH 20D 20D taught by Professor Eggers,john during the Fall '09 term at UCSD.
 Fall '09
 Eggers,John

Click to edit the document details