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

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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: A ( ) = det bracketleftbigg 5- 3 3 5- bracketrightbigg = (5- ) 2- 9 = 2- 10 + 16 = ( - 8)( - 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: A ( ) = det - 3 1 3- 2 1 2- =- vextendsingle vextendsingle vextendsingle vextendsingle- 2 2- vextendsingle vextendsingle vextendsingle vextendsingle- 3 vextendsingle vextendsingle vextendsingle vextendsingle 3 2 1- vextendsingle vextendsingle vextendsingle vextendsingle + vextendsingle vextendsingle vextendsingle vextendsingle 3- 1 2 vextendsingle vextendsingle vextendsingle vextendsingle =- ( 2- 4)- 3(- 3 - 2) + 6 + =- 3 + 14 + 12 ....
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5.2soln - Solutions to problems from section 5.2 2. Find...

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