Quiz+19+solution

Quiz+19+solution - MATH 17100 28446 Quiz 19 solution 11/30/...

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MATH 17100 28446 Quiz 19 solution 11/30/ 2009 1. For the matrix 314 026 005   =  A , find (i) The eigenvalues (ii) The corresponding eigenvectors Characteristic equation, 3 14 det( ) det 0 2 6 (3 )(2 )(5 ) 0 0 05 λ λλλ = = −= AI 3, 2, 5 ⇒= For (1) 1 3, suppose corresponding eigenvector is = v 33 1 4 0 1 4 010 0 23 6 0 16 001 0 0 53 0 0 2 000   →−  (1) (1) 23 and vv are basic variables and (1) 1 v is a free variable (1) 1 , arbitrary v αα (1) (1) 0 and 0 (1) 1 (1) (1) 2 (1) 3 1 00 v v v α     = =   v For (2) 2 2, suppose corresponding eigenvector is = v 32 1 4 114 110 0 22 6 006 0 0 52 003 −→
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(2) 13 and vv are basic variables and 2 v is a free variable 2 , arbitrary v ββ ⇒= 12 3 and 0 v = 1 2 3 1 1 00 v v v β  −−        = =     v For (3) 3 5, suppose corresponding eigenvector is λ = v 3 5 14 2 1 41 1 / 2 21 0 3 0 25 6 0 36 0 1 2 01 2 0 0 55 0 0 0 0 0 0 00 0
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This note was uploaded on 11/04/2010 for the course MATH 17100 taught by Professor Kitchens during the Spring '10 term at IUPUI.

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Quiz+19+solution - MATH 17100 28446 Quiz 19 solution 11/30/...

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