# q7 - v 1 = 1 1 For Î =-5 we need the null space for 3 5 4...

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MA366 Sathaye Quiz 7 Name Sec. Row Find the general solution of the system: X 0 = 3 4 8 - 1 ! X . Be sure to show all work. Answer: The equation is X 0 = AX where the char. poly. of A is: ± ± ± ± ± 3 - λ 4 8 - 1 - λ ± ± ± ± ± = λ 2 - 2 λ - 35 . Its roots are 7 , - 5. For λ = 7 we need the null space for 3 - 7 4 8 - 1 - 7 ! and this is seen to give a solution
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Unformatted text preview: v 1 = 1 1 ! . For Î» =-5 we need the null space for 3 + 5 4 8-1 + 5 ! and this is seen to give a solution v 2 = 1-2 ! . The general solution is: X = c 1 e 7 t v 1 + c 2 e-5 t v 2 = c 1 e 7 t 1 1 ! + c 2 e-5 t 1-2 ! ....
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## This note was uploaded on 01/18/2012 for the course MATH 366 taught by Professor Edraygoins during the Fall '09 term at Purdue.

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