AMath350.F12.A6.Sol

# 0 2 1 0 1 2 1 2 0 0 1 0 so two linearly independent

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Unformatted text preview: d v2 are linearly independent since 1 0 0 ) 1+ 0=0 1 1 = 2 = 0. 0 +2 1 = 0 ) 1 2 1 = 2 = 0. 0 1 0 So two linearly independent solutions of the system are y1 (x) = e 5x v1 and y2 (x) = e 5x v2 So two linearly independent solutions of the system are y1 (x) = e 5x v1 and y2 (x) = e 5x v2 c e 5x 5x and the general solution is y = c1 e 5x v1 + c2 e 5x v2 = c1 e 5x . 1 and the general solution is y = c1 e 5x v1 + c2 e 5x v2 = c2 e 5x . c2 e (b) In component form, the system becomes (b) In component form, the system becomes 0 y10 = 5 y1 y01 = 5 y1 . y20 = 5y2 . y2 = 5 y2 5. (a) A = 5. (a) A = 2 2 AMATH 350 Assignment #6 Solutions - Fall 2012 Page 4 AMATH 350 Figure 1: Assignment #6 Solutions - Fall 2012 Page 5 AMATH 350 Figure 2: Assignment #6 Solutions - Fall 2012 Page 6 AMATH 350 Figure 3: Assignment #6 Solutions - Fall 2012 Page 7...
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