MAT2705-01 08F 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 arrows and equal signs 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). You may use technology to find the roots of polynomials. [No mercy for mistakes here.]
1. 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 .a) Rewrite this system of DEs and its initial conditions in matrix form for the vector variable 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 , identifying the coefficient matrix A.b) By hand showing all steps, find the standard eigenvectors 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 produced by the solution algorithm with eigenvalues ordered in decreasing order. Evaluate the matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYjUSFGJy9GM1Enbm9ybWFsRic= =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and its inverse, and the diagonal matrix 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.
c) Write out the new matrix DE for 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, namely 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, and write out and solve the three decoupled equations for the new scalar variables, then reconstruct the general solution LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkmbW92ZXJHRiQ2JS1GIzYnLUkjbWlHRiQ2J1EieEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGNi8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRidGNEY3RjlGPC1JI21vR0YkNi5RLSZSaWdodEFycm93O0YnLyUscGxhY2Vob2xkZXJHRjYvRjpRJ25vcm1hbEYnLyUmZmVuY2VHUSZ1bnNldEYnLyUqc2VwYXJhdG9yR0ZJLyUpc3RyZXRjaHlHRjYvJSpzeW1tZXRyaWNHRkkvJShsYXJnZW9wR0ZJLyUubW92YWJsZWxpbWl0c0dGSS8lJ2FjY2VudEdGSS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlgvJSdhY2NlbnRHRjYtRkA2LVEiPUYnRkUvRkhRJmZhbHNlRicvRktGW28vRk1GW28vRk9GW28vRlFGW28vRlNGW28vRlVGW28vRldRLDAuMjc3Nzc3OGVtRicvRlpGY28tSSVtc3VwR0YkNiUtRjE2JVEiQkYnRjcvRjpRJ2l0YWxpY0YnLUYjNiQtRjE2I1EhRidGRS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRkA2LVEifkYnRkVGam5GXG9GXW9GXm9GX29GYG9GYW9GVkZZLUYsNiUtRiM2Jy1GMTYnUSJ5RidGNEY3RjlGPEY0RjdGOUY8Rj9GZW5GRQ==.d) Solve the initial conditions using matrix methods to find the IVP solution 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.
e) Plot 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 on the same axes in an appropriate window and sketch what you see, labeling axes and tickmarks and curves. Find the value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= at which the two variables are equal. This can be done easily exactly using rules of exponents, but if you have trouble, find the numerical solution. What is this common value at that time?f) Optional. [translate: read the answer key to see the picture].
On the grid provided, indicate by thick arrows both eigenvectors, extending them to labeled coordinate 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 axes, and draw in the vector LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EieEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGMS8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRictSShtZmVuY2VkR0YkNiQtRiM2JC1JI21uR0YkNiRRIjBGJy9GNVEnbm9ybWFsRidGQ0ZDRkM= and its parallelogram projection onto those axes. Evaluate the new coordinates of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EieEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGMS8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRictSShtZmVuY2VkR0YkNiQtRiM2JC1JI21uR0YkNiRRIjBGJy9GNVEnbm9ybWFsRidGQ0ZDRkM= using matrix methods. Do their values seem consistent with your drawing? Explain.JSFH solution1.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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 times the first eigenvector (first quadrant) minus 8 times the second eigenvector (second quatrant) equals the vector [5,-5].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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=TTdSMApJNVJUQUJMRV9TQVZFLzUwNjY4OTI4WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjJSIjIiMhIigiIiciIiIhIic2Ig==TTdSMApJNVJUQUJMRV9TQVZFLzUxMDA1NDYwWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjISIlISIqNiI=TTdSMApJNVJUQUJMRV9TQVZFLzUxMTAxNjIwWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjJSIjIiMjIiIiIiIkRigjISIiIiIjRig2Ig==TTdSMApJNVJUQUJMRV9TQVZFLzUxMTA1ODIwWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjJSIjIiMjIiInIiImIyEiJ0YpIyIiJEYpIyIiI0YpNiI=TTdSMApJNVJUQUJMRV9TQVZFLzUxMTA5NjkyWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjLCYtJSRleHBHNiMsJCUidEchIioiIiUtRik2IywkRiwhIiUiIiIsJkYoISIpRi8iIiQ2Ig==