141Bquiz4csols

141Bquiz4csols - 1 MATH 141B QUIZ#4 Solutions Date Mon...

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Unformatted text preview: 1 MATH 141B QUIZ#4 Solutions Date: Mon Feb 12, 2008 Instructor: Dr. M.Fabbri 1. i) False . The characteristic equation is det( A- rI ) = vextendsingle vextendsingle vextendsingle vextendsingle- 3- r 2 1- 4- r vextendsingle vextendsingle vextendsingle vextendsingle = (3 + r )(4 + r )- 2 = r 2 + 7 r + 10 = 0 . ii) True . Since r 2 + 7 r + 10 = ( r + 5)( r + 2) we get r 1 =- 5 and r 2 =- 2 . iii) True . bracketleftbigg- 3 2 1- 4 bracketrightbiggbracketleftbigg- 1 1 bracketrightbigg = bracketleftbigg 5- 5 bracketrightbigg =- 5 bracketleftbigg- 1 1 bracketrightbigg . Therefore, C) is the answer. 2. i) True . The characteristic equation is 0 = det( A- rI ) vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle 3- r- 2 2- r 1- 2 3- r vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle = [(3- r ) 2 (2- r ) + 0 + 0]- [4(2- r ) + 0 + 0] = (2- r )[(3- r ) 2- 4] = (2- r )( r 2- 6 r + 5) = (2- r )( r- 5)( r- 1) and therefore, we get 3 distinct eigenvalues...
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This note was uploaded on 03/30/2008 for the course MATH 141B taught by Professor Marcfabbri during the Spring '08 term at Penn State.

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141Bquiz4csols - 1 MATH 141B QUIZ#4 Solutions Date Mon...

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