MAT2705-02/05 15S Quiz 6 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). [You should use technology for row reductions and determinants. Report results you find in this way: reduced matrix, value of det.]
1. a) Find the general solution of the following linear system, identifying your coefficient matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, the right hand side vector 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 the augmented matrix 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, the RREF matrix and give the solution in scalar form: 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.
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b) Write the solution in the column matrix vector form 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 , where the first term is a particular solution and the second term is the general solution of the corresponding homogeneous system with 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 .c) Identify a basis of the solution space of the related homogeneous system. [Write your basis using curly brace set notation, using either angle bracket vector notation or column matrix notation.]d) Consider the set of vectors {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} which form the columns of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. What are the independent relationships among these vectors that follow immediately from the reduced form of the matrix? (Rewrite each such relationship in the form: a linear combination of them equals the zero vector.)e) Identify a basis of the span of the set of vectors {LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUklbXN1YkdGJDYmLUkmbW92ZXJHRiQ2JS1GIzYnLUYsNiUtSSNtaUdGJDYnUSJ2RicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR0Y7LyUsbWF0aHZhcmlhbnRHUSxib2xkLWl0YWxpY0YnLyUrZm9udHdlaWdodEdRJWJvbGRGJy1GIzYlLUkjbW9HRiQ2LVEhRicvRj9RJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZOLyUpc3RyZXRjaHlHRk4vJSpzeW1tZXRyaWNHRk4vJShsYXJnZW9wR0ZOLyUubW92YWJsZWxpbWl0c0dGTi8lJ2FjY2VudEdGTi8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRmduRjwvRj9RJ2l0YWxpY0YnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGOUY8Rj5GQS1GRzYuUS0mUmlnaHRBcnJvdztGJy8lLHBsYWNlaG9sZGVyR0Y7RkovRk1RJnVuc2V0RicvRlBGZW8vRlJGOy9GVEZlby9GVkZlby9GWEZlby9GWkZlby9GZm5RJjAuMGVtRicvRmluRl1wL0ZaRjstRiM2JS1JI21uR0YkNiRRIjFGJ0ZKRjxGam5GXG8vSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJ0ZGLUZHNi1RIixGJ0ZKRkwvRlBGO0ZRRlNGVUZXRllGXHAvRmluUSwwLjMzMzMzMzNlbUYnLUZHNi1RIn5GJ0ZKRkxGT0ZRRlNGVUZXRllGXHBGXnAtRkc2LVEjLi5GJ0ZKRkxGT0ZRRlNGVUZXRlkvRmZuUSwwLjIyMjIyMjJlbUYnRl5wLUZHNi1RIi5GJ0ZKRkxGT0ZRRlNGVUZXRllGXHBGXnBGX3FGaXBGX3EtRiw2JS1GLzYlLUYjNidGNUY5RjxGPkZBLUZHNi5GYW9GYm9GSkZMRk9GZ29GU0ZVRldGWUZlbkZobkZfcC1GIzYmLUZjcDYkUSI0RidGSkY8RmJvRmpuRlxvRko=} from the leading columns of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.
2. No two of the following sets of three vectors are proportional, so at most there might be one linear relationship among them. If appropriate, use the determinant to determine if they are linearly independent, justifying your conclusion. If linearly dependent, use the row reduced echelon form of their matrix of corresponding columns to write down single independent relationship among them and rewrite it in the form of an integer coefficient linear combination of these vectors equaling the zero vector. Double check that you have entered the vectors correctly.
a) {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b) {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},
c) {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,
.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1.Here we set up the vectors:Qys+SSN2MUc2Ii1JJDwsPkdGJTYlIiIkIiIiIiIjRio+SSN2MkdGJS1GJzYlIiImRishIiJGKj5JI3YzR0YlLCZGJEYqRi0hIiNGKj5JI3Y0R0YlLCZGJEYrRjNGKkYqPkkiYkdGJSwqRiRGMUYtRipGM0YxRjdGKg==PkkiQUc2Ii1JJDx8Z3I+R0YkNiZJI3YxR0YkSSN2MkdGJEkjdjNHRiRJI3Y0R0YkLy1JMGRlbGF5RG90UHJvZHVjdEc2JCUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nRzYkRiZJKF9zeXNsaWJHRik2JUkiQUdGKS0mSSdWZWN0b3JHRis2I0knY29sdW1uR0YpNiMvSSQlaWRHRikiNUUudiJ5dVN1WSU9SSV0cnVlR0YmSSJiR0YpLUkmc29sdmVHNiI2IzwlLywqJkkieEdGJDYjIiIiRiwmRio2IyIiI0YvJkYqNiMiIiQhIiQmRio2IyIiJSEiIkYyLywqRilGL0YtRjdGMEY2RjQiIilGLC8sKkYpRjJGLSIiJkYwISIoRjRGN0Y6LUkkPHxncj5HSShfc3lzbGliRzYiNiRJIkFHRiVJImJHRiU=Qyc+SSJDRzYiLUkkPHxncj5HSShfc3lzbGliR0YlNiRJIkFHRiVJImJHRiUiIiItSTZSZWR1Y2VkUm93RWNoZWxvbkZvcm1HRiU2I0YkRiwvLSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0YoNiNJJ2NvbHVtbkdGJTYjL0kkJWlkR0YlIjVxZXUieXVTdVklPS1JM0JhY2t3YXJkU3Vic3RpdHV0ZUdGJTYjSSIlR0YlThis is the vector form of the solution, but we would reverse the order of the parameters, working from top down instead of bottom up like Maple.
The general solution in scalar form (reversing order of parameters as we do by hand):
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Basis of the homogeneous solution space: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The first two vectors are a basis of the span of all of these vectors.JSFH2.a) 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third column is the first minus twice the second, so the same relationship applies to the original vectors.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 the determinant is nonzero/zero they are linearly independent/dependent.
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independent.c) 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dependent. The third is 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 times the first plus 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 times the second:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZHLUkjbWlHRiQ2KFEjdjNGJy8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUlYm9sZEdRJmZhbHNlRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRIj1GJ0YvRjJGOC9GPFEnbm9ybWFsRicvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZULUY/NjBRKiZ1bWludXMwO0YnRi9GMkY4RkJGREZGRkhGSkZMRk5GUC9GU1EsMC4yMjIyMjIyZW1GJy9GVkZlbi1JJm1mcmFjR0YkNiktSSNtbkdGJDYnUSIzRidGL0YyRjhGQi1GIzYoLUZbbzYnUSI1RidGL0YyRjhGQkYvRjJGNUY4RjsvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmhvLyUpYmV2ZWxsZWRHRjRGOC1GPzYwUSJ+RidGL0YyRjhGQkZERkZGSEZKRkxGTkZQL0ZTUSYwLjBlbUYnL0ZWRmFwLUYsNihRI3YxRidGL0YyRjVGOEY7LUY/NjBRKCZtaW51cztGJ0YvRjJGOEZCRkRGRkZIRkpGTEZORlBGWkZmbi1GaG42KS1GW282J0Zlb0YvRjJGOEZCRl5vRmNvRmZvRmlvRltwRjgtRj82MUZfcEYvRjJGOC8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RidGQkZERkZGSEZKRkxGTkZQRmBwRmJwLUYsNilRI3YyRidGL0YyRjVGOEZfcUY7LUY/NjFRIjtGJ0YvRjJGOEZfcUZCRkQvRkdGN0ZIRkpGTEZORlBGYHBGVS1GW282KEZdb0YvRjJGOEZfcUZCRl1xLUYsNilGZXBGL0YyRjVGOEZfcUY7LUY/NjFRIitGJ0YvRjJGOEZfcUZCRkRGRkZIRkpGTEZORlBGWkZmbkZicUZdci1GW282KEZib0YvRjJGOEZfcUZCRl1xLUYsNilGLkYvRjJGNUY4Rl9xRjstRj82MUZBRi9GMkY4Rl9xRkJGREZGRkhGSkZMRk5GUEZSRlUtRltvNihRIjBGJ0YvRjJGOEZfcUZCRmVxRl1xRmlxRl1xLUkobWZlbmNlZEdGJDYqLUYjNi0tRltvNihRIjJGJ0YvRjJGOEZfcUZCLUY/NjFRIixGJ0YvRjJGOEZfcUZCRkRGaHFGSEZKRkxGTkZQRmBwL0ZWUSwwLjMzMzMzMzNlbUYnRmZyRmFzLUY/NjFGWUYvRjJGOEZfcUZCRkRGRkZIRkpGTEZORlBGWkZmbkZpcUYvRjJGOC8lK2V4ZWN1dGFibGVHRjRGQkYvRjJGOEZfcUZCLyUlb3BlbkdRJyZsYW5nO0YnLyUmY2xvc2VHUScmcmFuZztGJ0Zdci1GanI2Ki1GIzYuLUZbbzYoUSI0RidGL0YyRjhGX3FGQkZhc0Zmc0ZgckZhc0Zmcy1GW282KFEiNkYnRi9GMkY4Rl9xRkJGL0YyRjhGX3FGQkYvRjJGOEZfcUZCRmpzRl10Rl1yRmByLUZqcjYqLUYjNi1GZnNGXnNGYXMtRltvNihGZW9GL0YyRjhGX3FGQkZhc0ZpcUYvRjJGOEZfcUZCRi9GMkY4Rl9xRkJGanNGXXRGL0YyRjhGaHNGQg==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0NzgxNzQ5MzY2WColKWFueXRoaW5nRzYiRiVbZ2whIyUhISEiJCIkIiIkIiIiIiIjRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0NzgxNzQ5NjA2WColKWFueXRoaW5nRzYiRiVbZ2whIyUhISEiJCIkIiImIiIjISIiRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0NzgxNzQ5NzI2WColKWFueXRoaW5nRzYiRiVbZ2whIyUhISEiJCIkISIoISIkIiIlRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0NzgxNzQ5ODQ2WColKWFueXRoaW5nRzYiRiVbZ2whIyUhISEiJCIkISIiRiYiIilGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0NzgxNzQ5OTY2WColKWFueXRoaW5nRzYiRiVbZ2whIyUhISEiJCIkIiIpIiIkIiIiRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0NzgxNzUwMjA2WCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjLSIkIiUiIiQiIiIiIiMiIiZGKCEiIiEiKCEiJCIiJUYqRioiIilGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0NzgxNzUwNDQ2WColKWFueXRoaW5nRzYiRiVbZ2whIyUhISEiJCIkLColI3gxRyIiJCUjeDJHIiImJSN4M0chIiglI3g0RyEiIiwqRiciIiJGKSIiI0YrISIkRi1GLiwqRidGMUYpRi5GKyIiJUYtIiIpRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0NzgxNzUyMjQ2WCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjMCIkIiYiIiQiIiIiIiMiIiZGKCEiIiEiKCEiJCIiJUYqRioiIilGLkYmRidGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0NzgxNzQ1OTkwWCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjMCIkIiYiIiQiIiIiIiMiIiZGKCEiIiEiKCEiJCIiJUYqRioiIilGLkYmRidGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0NzgxNzQ2NzEwWCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjMCIkIiYiIiIiIiFGJ0YnRiZGJ0YmISIjRiciIiRGKEYnRiZGJkYnRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0NzgxNzQ1ODcwWColKWFueXRoaW5nRzYiRiVbZ2whIyUhISEiJSIlJSV4X18xRyUleF9fMkclJXhfXzNHJSV4X180R0YlTTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0NzgxNzQ4MTUwWColKWFueXRoaW5nRzYiRiVbZ2whIyUhISEiJSIlLCgiIiJGJyYlI190RzYjIiIjISIiJkYpNiNGJyEiJCwoRidGJ0YoRitGLUYrRihGLUYl