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Unformatted text preview: Math 330 Homework 5.2 (Pages 317,318) (8) Find the characteristic polynomial and the eigenvalues of the matrix A = bracketleftBigg 7 2 2 3 bracketrightBigg SOLUTION: The eigenvalues λ must satisfy det( A λI ) = 0: 0 = vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle 7 λ 2 2 3 λ vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle = (7 λ )(3 λ ) (2)( 2) = λ 2 3 λ 7 λ + 21 + 4 ⇒ λ 2 10 λ + 25 = 0 ⇒ ( λ 5) 2 = 0 So λ = 5 is the only eigenvalue. 1 (12) Find the characteristic polynomial of the matrix below: A =  1 0 1 3 4 1 0 2 SOLUTION: We calculate the determinant by expanding along the 3rd row:  A λI  = vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle 1 λ 1 3 4 λ 1 2 λ vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle = (2 λ ) vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle 1 λ 3 4 λ vextendsingle vextendsingle vextendsingle...
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This note was uploaded on 09/19/2009 for the course MATH 330 taught by Professor Johnson,j during the Spring '08 term at Nevada.
 Spring '08
 Johnson,J
 Math, Linear Algebra, Algebra

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