5.2soln - Solutions to problems from section 5.2 2 Find the...

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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.

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5.2soln - Solutions to problems from section 5.2 2 Find the...

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