MAT2705-04/05 22S Quiz 4 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). Only use technology to CHECK hand calculations, not subsitute for them, unless specifically requested.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
a) Write down the coefficient matrix A, the RHS matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkmbW92ZXJHRiQ2JS1GIzYmLUkjbWlHRiQ2KFEiYkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStleGVjdXRhYmxlR0Y5LyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y+RjovJTBmb250X3N0eWxlX25hbWVHUSVUZXh0RicvRj1RJ25vcm1hbEYnLUYxNiNRIUYnLyUnYWNjZW50R0Y2RkZGOkZE and the augmented matrix C = <A | LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JUYrLUkmbW92ZXJHRiQ2JS1GIzYoLUYsNidRImJGJy8lJWJvbGRHUSV0cnVlRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0ZBL0Y9RjsvJStmb3JlZ3JvdW5kR1ErWzAsMTYwLDgwXUYnLyUscGxhY2Vob2xkZXJHRjsvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHRjsvRkBRJ2l0YWxpY0YnRisvJSdhY2NlbnRHRjsvRkBRJ25vcm1hbEYnRitGUA==> for this linear system of equations.b) Use the LinearSolveTutor to reduce this augmented matrix step by step to its ReducedRowEchelonForm avoiding fractions as much as possible), recording the intermediate matrices and row operations for each step (as in LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYwLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RMSZMZWZ0UmlnaHRBcnJvdztGJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaLUYsNiVGLi1GIzYmLUY+NiVRIjJGJ0Y1RkFGMkY1RjhGQy1GRzYuUSIsRidGNUZBRkovRk1GNC9GT0Y3RlBGUkZURlYvRllRJjAuMGVtRicvRmZuUSwwLjMzMzMzMzNlbUYnLUYsNiVGLi1GIzYlLUY+NiVRIjNGJ0Y1RkFGNUZBRkMtRkc2LlEoJnNyYXJyO0YnRjVGQUZKRkxGYm9GUEZSRlRGVkZjby9GZm5GZG9GZ28tRkc2LlEiK0YnRjVGQUZKRkxGYm9GUEZSRlRGVi9GWVEsMC4yMjIyMjIyZW1GJy9GZm5GZnBGW28tRkc2LlEifkYnRjVGQUZKRkxGYm9GUEZSRlRGVkZjb0ZhcC1GLDYlRi4tRiM2JUY9RjVGQUZDRl5vRjVGQQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGNUZBLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYuUSgmc3JhcnI7RidGNUZBLyUmZmVuY2VHRjcvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGWi1JJm1mcmFjR0YkNihGPS1GIzYlLUY+NiVRIjJGJ0Y1RkFGNUZBLyUubGluZXRoaWNrbmVzc0dGQC8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zjby8lKWJldmVsbGVkR0Y3LUZHNi5RIn5GJ0Y1RkFGSkZMRk5GUEZSRlRGVkZYRmVuRistRi82I1EhRidGNUZB) or just copy the output to a blank worksheet, print it on paper, and attach to this quiz to include in your scan.
c) Write out the equations that correspond to the reduced matrix. Identify the leading variables (L) and the free variables (F) and solve. State your solution in the scalar form: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjFGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GLzYjUSFGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRjw= = ..., LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRj4vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GLzYjUSFGJ0ZARj4= = ..., etc , then write in column matrix form and identify the coefficient vectors 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 of your free variable parameters 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 and the constant term vector d in the form 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 .
d) Enter the augmented matrix into Maple and by right context panel menu, find the reduced matrix and the solution of the system of equations. Write down exactly what Maple gives you for the column matrix solution and compare with your reduced matrix and solution. They should agree. Do they? How do the parameter symbols correspond?solutionFrom the textbook 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can solve these to express the first three variables in terms of the last two.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYxLUkjbWlHRiQ2KVEmc29sdmVGJy8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUlYm9sZEdRJmZhbHNlRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYxUSIoRidGL0YyRjhGOy9GPlEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjE2NjY2NjdlbUYnLyUncnNwYWNlR0ZWLUZBNjFRIn5GJ0YvRjJGOEY7RkQvRkdGNEZIL0ZLRjRGTEZORlBGUi9GVVEmMC4wZW1GJy9GWEZpbi1GQTYxUSJ8ZnJGJ0YvRjJGOEY7RkRGRkZIRkpGTEZORlBGUkZURldGWS1JKG1hY3Rpb25HRiQ2JS1JKm12ZXJiYXRpbUdGJDYjUWRibDYlLywsKiYiIiMiIiImSSJ4RzYiNiMiIiIiIiIiIiIqJiIiJSIiIiZJInhHNiI2IyIiIyIiIiIiIiZJInhHNiI2IyIiJCEiIiomIiIjIiIiJkkieEc2IjYjIiIlIiIiISIiKiYiIiMiIiImSSJ4RzYiNiMiIiYiIiIiIiIiIicvLCwmSSJ4RzYiNiMiIiIiIiIqJiIiJCIiIiZJInhHNiI2IyIiIyIiIiIiIiomIiIjIiIiJkkieEc2IjYjIiIkIiIiIiIiKiYiIigiIiImSSJ4RzYiNiMiIiUiIiIhIiIqJiIiJCIiIiZJInhHNiI2IyIiJiIiIiIiIiIiKi8sLComIiImIiIiJkkieEc2IjYjIiIiIiIiIiIiKiYiIikiIiImSSJ4RzYiNiMiIiMiIiIiIiIqJiIiKCIiIiZJInhHNiI2IyIiJCIiIiEiIiomIiInIiIiJkkieEc2IjYjIiIlIiIiIiIiJkkieEc2IjYjIiImIiIiIiIlRicvJSthY3Rpb250eXBlR1E6bWFwbGVzb2Z0LmNvbTpsYWJlbChMMjk1KUYnLyUldmlld0dRJmxhYmVsRidGWS1GQTYxUSJ8aHJGJ0YvRjJGOEY7RkRGRkZIRkpGTEZORlBGUkZUL0ZYUSwwLjExMTExMTFlbUYnRlktRkE2MVEiKUYnRi9GMkY4RjtGREZGRkhGSkZMRk5GUEZSRlRGV0YvRjJGOEY7RkQ=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYyLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRL0dlbmVyYXRlTWF0cml4RidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNictRlM2Ji1GIzYlLUYsNiVRJHN5c0YnRi9GMi8lK2V4ZWN1dGFibGVHRj1GOUY5LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnLUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkgvRktRJjAuMGVtRicvRk5RLDAuMzMzMzMzM2VtRictRlM2Ji1GIzYtLUklbXN1YkdGJDYlLUYsNiVRInhGJ0YvRjItRiM2JC1JI21uR0YkNiVRIjFGJ0ZobkY5RjkvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Zgby1GXXA2JUZfcC1GIzYkLUZlcDYlUSIyRidGaG5GOUY5RmhwRmBvLUZdcDYlRl9wLUYjNiQtRmVwNiVRIjNGJ0ZobkY5RjlGaHBGYG8tRl1wNiVGX3AtRiM2JC1GZXA2JVEiNEYnRmhuRjlGOUZocEZgby1GXXA2JUZfcC1GIzYkLUZlcDYlUSI1RidGaG5GOUY5RmhwRmhuRjlGOUZqbkZdb0ZobkY5RjktRjY2LVEiO0YnRjlGO0Zjb0ZARkJGREZGRkhGZG9GTS1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR0Zlby8lJmRlcHRoR0Zfcy8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIRmRvL0ZORmVvLUYsNiVRIkFGJ0YvRjJGYG8tRiw2JVEiYkYnRi9GMkY1Rk8tRlM2JC1GIzYmLUZTNiYtRiM2JEZlbkY5RjlGam5GXW9GYG8tRlM2Ji1GIzYsRlxwRmBvRltxRmBvRmJxRmBvRmlxRmBvRmByRjlGOUZqbkZdb0Y5RjktRiw2I1EhRidGaG5GOQ==If we want to augment the last two together, we recover the first one.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so the variables are:
Leading: 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
Free: 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 the solution 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We used the parameter names 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.