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Unformatted text preview: Solutions to problems from section 5.2 2. Find the characteristic polynomial and the eigenvalues of the matrix A = bracketleftbigg 5 3 3 5 bracketrightbigg . Solution: χ A ( λ ) = det bracketleftbigg 5 λ 3 3 5 λ bracketrightbigg = (5 λ ) 2 9 = λ 2 10 λ + 16 = ( λ 8)( λ 2) . Therefore the eigenvalues of A are 8 and 2 (both with multiplicity one). 10. Find the characteristic polynomial of the matrix A = 0 3 1 3 0 2 1 2 0 . Solution: χ A ( λ ) = det  λ 3 1 3 λ 2 1 2 λ = λ vextendsingle vextendsingle vextendsingle vextendsingle λ 2 2 λ vextendsingle vextendsingle vextendsingle vextendsingle 3 vextendsingle vextendsingle vextendsingle vextendsingle 3 2 1 λ vextendsingle vextendsingle vextendsingle vextendsingle + vextendsingle vextendsingle vextendsingle vextendsingle 3 λ 1 2 vextendsingle vextendsingle vextendsingle vextendsingle = λ ( λ 2 4) 3( 3 λ 2) + 6 + λ = λ 3 + 14 λ + 12 ....
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This note was uploaded on 01/28/2010 for the course MATH 307 taught by Professor Axenovich during the Fall '08 term at Iowa State.
 Fall '08
 AXENOVICH

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