MAT2705-02/04 16F Quiz 8 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).
1. 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 ,
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 .JSFHa) Enter this IVP into Maple using "LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEjeDFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHRjEvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjVRJ25vcm1hbEYn" etc for the subscripted variables to avoid wasting time with subscripts. Right click and solve the system and write down the vector solution LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkmbW92ZXJHRiQ2JS1GIzYnLUkjbWlHRiQ2J1EieEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGNi8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRidGNEY3RjlGPC1JI21vR0YkNi5RLiZSaWdodFZlY3RvcjtGJy8lLHBsYWNlaG9sZGVyR0Y2L0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmdW5zZXRGJy8lKnNlcGFyYXRvckdGSS8lKXN0cmV0Y2h5R0Y2LyUqc3ltbWV0cmljR0ZJLyUobGFyZ2VvcEdGSS8lLm1vdmFibGVsaW1pdHNHRkkvJSdhY2NlbnRHRkkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZYL0ZVRjYtRkA2LVEiPUYnRkUvRkhRJmZhbHNlRicvRktGam4vRk1Gam4vRk9Gam4vRlFGam4vRlNGam4vRlVGam4vRldRLDAuMjc3Nzc3OGVtRicvRlpGYm8tSShtZmVuY2VkR0YkNiYtRiM2KS1GMTYjUSdgeF9fMWBGJy1GQDYtUSIsRidGRUZpbi9GS0Y2RlxvRl1vRl5vRl9vRmBvRlYvRlpRLDAuMzMzMzMzM2VtRictRjE2I1EnYHhfXzJgRidGXHAtRjE2I1EnYHhfXzNgRicvJStleGVjdXRhYmxlR0ZqbkZFRkUvJSVvcGVuR1EnJmxhbmc7RicvJSZjbG9zZUdRJyZyYW5nO0YnRmhwRkU= from Maple's output. Rewrite this as a linear combination of the two independent exponential functions which enter into that solution, whose coefficients are constant vectors, i.e., 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.b) Rewrite this system of DEs and its initial conditions explicitly in matrix form for the vector variable 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 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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].c) For this LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn, using Maple (Rightclick, Eigenvalues etc, Eigenvectors) write down the eigenvalues 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 (ordered by increasing value, they are integers!) and corresponding matrix of eigenvectors LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn =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 that it provides you, reordering them if necessary to order them as requested.d) Use technology to evaluate and write down the inverse matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1cEdGJDYlLUkjbWlHRiQ2JlEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNictSSNtb0dGJDYuUSomdW1pbnVzMDtGJ0Y1L0Y5USdub3JtYWxGJy8lJmZlbmNlR0Y3LyUqc2VwYXJhdG9yR0Y3LyUpc3RyZXRjaHlHRjcvJSpzeW1tZXRyaWNHRjcvJShsYXJnZW9wR0Y3LyUubW92YWJsZWxpbWl0c0dGNy8lJ2FjY2VudEdGNy8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlMtSSNtbkdGJDYlUSIxRidGNUZBRjJGNUY4LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GLzYjUSFGJ0Y1RkE= and use Maple to evaluate the matrix product LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtRi82JlEiQkYnRjJGNUY4RjJGNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYuUSI9RidGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZZLUklbXN1cEdGJDYlRj0tRiM2Jy1GRDYuUSomdW1pbnVzMDtGJ0Y1RkdGSUZLRk1GT0ZRRlNGVS9GWFEsMC4yMjIyMjIyZW1GJy9GZW5GX28tSSNtbkdGJDYlUSIxRidGNUZHRjJGNUY4LyUxc3VwZXJzY3JpcHRzaGlmdEdGQkYuLUZENi5RIn5GJ0Y1RkdGSUZLRk1GT0ZRRlNGVS9GWFEmMC4wZW1GJy9GZW5GW3BGPUY1Rkc=. Write down this result. Compare it to the corresponding list of eigenvalues in the same order as the eigenvectors.e) Given that 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, if 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 , use the inverse matrix to find 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, showing the matrix multiplication steps by hand (to prove that you actually know how to multiply a vector by a matrix, but check with Maple!). 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aXRoRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiYtRiw2JVEoU3R1ZGVudEYnRi9GMi1GUzYmLUYjNiUtRiw2JVEuTGluZWFyQWxnZWJyYUYnRi9GMi8lK2V4ZWN1dGFibGVHRj1GOUY5LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRltvRjlGOUY1RltvRjk=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b)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)LUkwZGVsYXlEb3RQcm9kdWN0RzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHNiRGJUkoX3N5c2xpYkdGKDYkLUYjNiQqJC1JJ3J0YWJsZUdGJTYmOyIiIiIiJEYzNyU3JSMhIiIiIiNGNEY0NyUiIiFGNEY0NyVGNEY8RjQvSShzdWJ0eXBlR0YqSSdNYXRyaXhHRipGOS1GMTYmRjNGMzclNyUiIiYhIidGNTclIiInISIoRjU3JUZIRkZGOkY+RjA=d) LUkwZGVsYXlEb3RQcm9kdWN0RzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHNiRGJUkoX3N5c2xpYkdGKDYkKiQtSSdydGFibGVHRiU2JjsiIiIiIiRGMTclNyUjISIiIiIjRjJGMjclIiIhRjJGMjclRjJGOkYyL0koc3VidHlwZUdGKkknTWF0cml4R0YqRjctRi82JUYxNyVGMkY4IiImL0Y9JkknVmVjdG9yR0YqNiNJJ2NvbHVtbkdGKA==These are the new coordinates of the initial value vector.manual derivation of eigenvectors not required on this quizJSFHJSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVEnJiM5NTU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnRjIvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZJLUY2Ni1RIidGJ0YyRjlGO0Y9Rj9GQUZDRkUvRkhRLDAuMTExMTExMWVtRicvRktRJjAuMGVtRidGK0ZMLUY2Ni1RIjpGJ0YyRjlGO0Y9Rj9GQUZDRkVGR0ZKLyUrZXhlY3V0YWJsZUdGMUYyLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY6LUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZ1bWludXMwO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZMLUYsNiVRJyYjOTU1O0YnL0YwRj1GOS1GNjYtUScmc2RvdDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GVy1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIRlZGWC1GLDYlUS9JZGVudGl0eU1hdHJpeEYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYlLUkjbW5HRiQ2JFEiM0YnRjkvJStleGVjdXRhYmxlR0Y9RjlGOS1GNjYtUSI7RidGOUY7L0Y/RjFGQEZCRkRGRkZIRlYvRk5RLDAuMjc3Nzc3OGVtRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdGVy8lJmRlcHRoR0ZfcC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJ0ZZLUYsNiVRLERldGVybWluYW50RidGL0YyLUZqbjYkLUYjNiUtRiw2JVEiJUYnRi9GMkZib0Y5RjlGZG9Gam9GWS1GLDYlUSdmYWN0b3JGJ0YvRjJGanBGZG9Gam9GWS1GLDYlUSZzb2x2ZUYnRi9GMi1Gam42JC1GIzYnRl5xLUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkgvRktGaW9GaG8tRl9vNiRRIjBGJ0Y5RmJvRjlGOUZib0Y5LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZHLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSIrRidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkktRiw2JVEvSWRlbnRpdHlNYXRyaXhGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUkjbW5HRiQ2JFEiM0YnRjJGMkYyLUY2Ni1RIjtGJ0YyRjkvRjxGUEY9Rj9GQUZDRkUvRkhRJjAuMGVtRicvRktRLDAuMjc3Nzc3OGVtRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdGW28vJSZkZXB0aEdGY28vJSpsaW5lYnJlYWtHUShuZXdsaW5lRictRjY2LVEifkYnRjJGOUY7Rj1GP0ZBRkNGRUZqbi9GS0Zbby1GLDYlUTZSZWR1Y2VkUm93RWNoZWxvbkZvcm1GJ0ZPRlEtRlQ2JC1GIzYlLUYsNiVRIiVGJ0ZPRlEvJStleGVjdXRhYmxlR0YxRjJGMkZmbkZeb0ZbcC1GVDYmLUYjNihGZnAtRjY2LVEifGdyRidGMkY5RjsvRj5GUEY/RkFGQ0ZFL0ZIUSwwLjExMTExMTFlbUYnL0ZLRmRxLUYsNiVRK1plcm9NYXRyaXhGJ0ZPRlEtRlQ2JC1GIzYnRlgtRjY2LVEiLEYnRjJGOUZpbkY9Rj9GQUZDRkVGam4vRktRLDAuMzMzMzMzM2VtRictRlk2JFEiMUYnRjJGaXBGMkYyRmlwRjJGMi8lJW9wZW5HUScmbGFuZztGJy8lJmNsb3NlR1EnJnJhbmc7RidGZm5GXm9GW3AtRiw2JVEzQmFja3dhcmRTdWJzdGl0dXRlRidGT0ZRRmJwRmZuRl5vRltwLUYsNiVRI2IyRidGT0ZRLUY2Ni1RKiZjb2xvbmVxO0YnRjJGOUY7Rj1GP0ZBRkNGRS9GSEZdb0Zcby1GLDYlUSVzdWJzRidGT0ZRLUZUNiQtRiM2Li1JJW1zdWJHRiQ2JS1GLDYlUSNfdEYnRk9GUS1GIzYlRmJyRk9GUS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUY2Ni1RIj1GJ0YyRjlGO0Y9Rj9GQUZDRkVGZHNGXG9GYnJGXXItRl10NiVGX3QtRiM2JC1GWTYkUSIyRidGMkYyRmR0Rmd0LUZZNiRGZnRGMkZdckZbcEZmcEZpcEYyRjJGZm5GW3AtRiw2JVEjYjFGJ0ZPRlFGYXNGZXMtRlQ2JC1GIzYsLUZddDYlRl90LUYjNiRGYnJGMkZkdEZndEZhdUZdckZqdEZndEZickZdci1GLDYlUSMlJUYnRk9GUUYyRjItRiw2I1EhRidGXm8tRl9vNiZGYW9GZG9GZm8vRmlvUSVhdXRvRidGYXZGaXBGMg==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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 result is the same as Maple gives, with the ordering -1,-1,3 of the eigenvalues and of the two eigenvectors for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LlEqJnVtaW51czA7RicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZFLUkjbW5HRiQ2JVEiMUYnRi9GMkYvRjI=.d)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TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MzY1MTQwMDE0WColKWFueXRoaW5nRzYiRiVbZ2whIyUhISEiJCIkIiIjISIiIiIkRiU=