MAT2705-04/05 18F Quiz 9 Print Name (Last, First) _________________________________|__Show all work, including mental steps, in a clearly organized way that speaks for itself. Use proper mathematical notation, identifying expressions by their proper symbols (introducing them if necessary), and use EQUAL SIGNS and arrows when appropriate. Always simplify expressions. BOX final short answers. LABEL parts of problem. Keep answers EXACT (but give decimal approximations for interpretation). Indicate where technology is used and what type (Maple, GC). Justify all claims.
1. 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 ,
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY1LUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYmLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EnTm9ybWFsRidGPi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkobWZlbmNlZEdGJDYkLUYjNiYtRjs2JEZIRj5GQEZDRj5GPi1JI21vR0YkNi1RIj1GJ0Y+LyUmZmVuY2VHRkIvJSpzZXBhcmF0b3JHRkIvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGXm8tRjs2JFEiNUYnRj4tRlE2LVEiLEYnRj5GVC9GV0Y0RlhGWkZmbkZobkZqbi9GXW9RJjAuMGVtRicvRmBvUSwwLjMzMzMzMzNlbUYnLUZRNi1RIn5GJ0Y+RlRGVkZYRlpGZm5GaG5Gam5GaG8vRmBvRmlvLUYsNiVGLi1GIzYmLUY7NiRRIjJGJ0Y+RkBGQ0Y+RkZGSUZQLUZRNi1RKiZ1bWludXMwO0YnRj5GVEZWRlhGWkZmbkZobkZqbi9GXW9RLDAuMjIyMjIyMmVtRicvRmBvRltxLUY7NiRRIjRGJ0Y+RmRvLUYsNiVGLi1GIzYmLUY7NiRRIjNGJ0Y+RkBGQ0Y+RkZGSUZQRmFvRkBGQ0Y+ .LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=a) Rewrite this system of DEs and its initial conditions explicitly in matrix form for the vector variable LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JUYrLUkmbW92ZXJHRiQ2JS1GLDYnUSJ4RicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR0Y5LyUsbWF0aHZhcmlhbnRHUSxib2xkLWl0YWxpY0YnLyUrZm9udHdlaWdodEdRJWJvbGRGJy1GIzYkLUkjbW9HRiQ2LVEuJlJpZ2h0VmVjdG9yO0YnL0Y9USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGTC8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0ZMLyUobGFyZ2VvcEdGTC8lLm1vdmFibGVsaW1pdHNHRkwvJSdhY2NlbnRHRkwvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZlbkZIRldGSC1GRTYtUSI9RidGSEZKRk0vRlBGTEZRRlNGVUZXRllGZm4tSShtZmVuY2VkR0YkNiYtRiM2KC1JJW1zdWJHRiQ2JS1GLDYlRjZGOi9GPVEnaXRhbGljRictRiM2JC1JI21uR0YkNiRRIjFGJ0ZIRkgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GRTYtUSIsRidGSEZKL0ZORjlGW29GUUZTRlVGVy9GWlEmMC4wZW1GJy9GZ25RLDAuMzMzMzMzM2VtRictRmJvNiVGZG8tRiM2JC1GW3A2JFEiMkYnRkhGSEZecEZhcC1GYm82JUZkby1GIzYlLUZbcDYkUSIzRidGSEY6RmZvRl5wRkhGSC8lJW9wZW5HUScmbGFuZztGJy8lJmNsb3NlR1EnJnJhbmc7RidGSA== as a column matrix (using the actual matrices, not their symbols), identifying the coefficient matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn and suppressing function notation in the DE [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].b) For this LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn, use Maple to write down the eigenvalues 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 (ordered by increasing value, they are integers!) and corresponding matrix of eigenvectors LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn =LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYnLUYjNiktSSVtc3ViR0YkNiUtRiM2Ki1JI21pR0YkNiNRIUYnLUYjNiZGNS1JJm1vdmVyR0YkNiUtRjY2KFEiYkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGQy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSxib2xkLWl0YWxpY0YnLyUrZm9udHdlaWdodEdRJWJvbGRGJy1JI21vR0YkNi9RLSZSaWdodEFycm93O0YnRkYvJSxwbGFjZWhvbGRlckdGQy9GSlEnbm9ybWFsRicvJSZmZW5jZUdRJnVuc2V0RicvJSpzZXBhcmF0b3JHRlkvJSlzdHJldGNoeUdGQy8lKnN5bW1ldHJpY0dGWS8lKGxhcmdlb3BHRlkvJS5tb3ZhYmxlbGltaXRzR0ZZLyUnYWNjZW50R0ZZLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGYm8vRl9vRkNGRkZVRjVGQUZERkZGSUZMLUYjNiUtSSNtbkdGJDYlUSIxRidGRkZVRkZGVS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUZQNi5RInxnckYnRkZGVS9GWEZIL0ZlbkZIRmZuL0ZpbkZIL0Zbb0ZIL0Zdb0ZIL0Zfb0ZIL0Zhb1EsMC4xMTExMTExZW1GJy9GZG9GaXAtRjE2JUYzLUYjNiUtRmlvNiVRIjJGJ0ZGRlVGRkZVRlxwRl9wLUYxNiUtRiM2J0Y1RjlGNUZGRlUtRiM2JS1GaW82JVEiM0YnRkZGVUZGRlVGXHBGRkZVRkZGVS8lJW9wZW5HUScmbGFuZztGJy8lJmNsb3NlR1EnJnJhbmc7RidGRkZV that it provides you, reordering them if necessary to order them as requested.c) Use technology to evaluate and write down the inverse matrix 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 and use Maple to evaluate the matrix product LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtRi82JlEiQkYnRjJGNUY4RjJGNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYuUSI9RidGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZZLUklbXN1cEdGJDYlRj0tRiM2Jy1GRDYuUSomdW1pbnVzMDtGJ0Y1RkdGSUZLRk1GT0ZRRlNGVS9GWFEsMC4yMjIyMjIyZW1GJy9GZW5GX28tSSNtbkdGJDYlUSIxRidGNUZHRjJGNUY4LyUxc3VwZXJzY3JpcHRzaGlmdEdGQkYuLUZENi5RIn5GJ0Y1RkdGSUZLRk1GT0ZRRlNGVS9GWFEmMC4wZW1GJy9GZW5GW3BGPUY1Rkc= (use periods for multiplication if necessary). Write down this result. Compare it to the corresponding list of eigenvalues in the same order as the eigenvectors.d) Given that 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, if 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 , use the inverse matrix to find 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 (integers!), showing the matrix multiplication intermediate step by hand (to prove that you actually know how to multiply a vector by a matrix, but check with Maple!). e) Then write down and solve the decoupled equations for 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 and use their initial values to express the solution of the initial value problem for the original variables and finally write down the scalar solution 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.f) Enter this IVP from the first two lines above into Maple using "LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEjeDFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJTBmb250X3N0eWxlX25hbWVHUSdOb3JtYWxGJy9GM1Enbm9ybWFsRic=" etc for the subscripted variables to avoid wasting time with subscripts, but otherwise exactly as written. Right context menu it and solve the system. Does it agree with your hand solution? If not, write down the Maple solution and try to find your error. 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 thisJust some Maple tricks for bob to generate the DEs from the matrix entries automatically.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)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c) rearrange eigenvalues from lowest to highest: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d) 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These are the new coordinates of the initial value vector.e)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 so LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY5LUkjbWlHRiQ2JlEjeTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RIidGJ0YyL0Y2USdub3JtYWxGJy8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMTExMTExMWVtRicvJSdyc3BhY2VHUSYwLjBlbUYnLUY5Ni5RIj1GJ0YyRjxGPkZARkJGREZGRkhGSi9GTVEsMC4yNzc3Nzc4ZW1GJy9GUEZWLUY5Ni5RKiZ1bWludXMwO0YnRjJGPEY+RkBGQkZERkZGSEZKL0ZNUSwwLjIyMjIyMjJlbUYnL0ZQRmZuLUkjbW5HRiQ2JVEiM0YnRjJGPC1GOTYuUSJ+RidGMkY8Rj5GQEZCRkRGRkZIRkovRk1GUUZPRistRjk2LlEiLEYnRjJGPEY+L0ZBRjFGQkZERkZGSEZKRl9vL0ZQUSwwLjMzMzMzMzNlbUYnLUYsNiZRI3kyRidGL0YyRjVGOEZSRlhGXG9GZm9GYG8tRiw2JlEjeTNGJ0YvRjJGNUY4RlItRmluNiVRIjJGJ0YyRjxGXG9GaW9GMkY8 with solutions 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 and the arbitrary constants are their initial values calculated above 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manual derivation of eigenvectors not required on this 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Maple orders the eigenvectors for a given eigenvalue in reverse order compared to our hand algorithm, identifying the free variables in order and the corresponding parameter vector coefficients in the same order, so we switched back to our order.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