MAT2705-03/04 11F 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 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).1. 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
a) Write down the coefficient matrix A, the RHS matrix 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 and the augmented matrix C = <A | 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> for this linear system of equations.b) With technology (identify your choice!), reduce this matrix C step by step to its ReducedRowEchelonForm avoiding fractions, recording the intermediate matrices and row operations for each step (as in LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RMSZMZWZ0UmlnaHRBcnJvdztGJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZJLyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRkkvJShsYXJnZW9wR0ZJLyUubW92YWJsZWxpbWl0c0dGSS8lJ2FjY2VudEdGSS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlgtRiw2JUYuLUYjNiUtRjs2JFEiMkYnRj5GMkY1RkAtRkQ2LVEiLEYnRj5GRy9GS0Y0L0ZNRklGTkZQRlJGVC9GV1EmMC4wZW1GJy9GWlEsMC4zMzMzMzMzZW1GJy1GLDYlRi4tRiM2JC1GOzYkUSIzRidGPkY+RkAtRkQ2LVEoJnNyYXJyO0YnRj5GR0ZKRmBvRk5GUEZSRlRGYW8vRlpGYm9GZW8tRkQ2LVEiK0YnRj5GR0ZKRmBvRk5GUEZSRlQvRldRLDAuMjIyMjIyMmVtRicvRlpGZHBGaW4tRkQ2LVEifkYnRj5GR0ZKRmBvRk5GUEZSRlRGYW9GX3AtRiw2JUYuLUYjNiRGOkY+RkBGXG9GPg==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0Y+LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUSgmc3JhcnI7RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGSS8lKXN0cmV0Y2h5R0ZJLyUqc3ltbWV0cmljR0ZJLyUobGFyZ2VvcEdGSS8lLm1vdmFibGVsaW1pdHNHRkkvJSdhY2NlbnRHRkkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZYLUkmbWZyYWNHRiQ2KEY6LUYjNiQtRjs2JFEiMkYnRj5GPi8lLmxpbmV0aGlja25lc3NHRj0vJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGYW8vJSliZXZlbGxlZEdGSS1GRDYtUSJ+RidGPkZHRkpGTEZORlBGUkZURlZGWUYrLUYvNiNRIUYnRj4=). You may do AddRow operations simultaneously.
c) Write out the equations that correspond to the reduced matrix. Identify the leading variables and the free variables and solve. State your solution in the scalar form: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjFGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GLzYjUSFGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRjw= = ..., LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRj4vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GLzYjUSFGJ0ZARj4= = ..., etc, then state this solution in column matrix ("vector") form 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 = ... . d) Optional. Now express your vector form of the solution in the following linear combination form: 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 depending on how many free parameters LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RIixGJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRkkvJSpzeW1tZXRyaWNHRkkvJShsYXJnZW9wR0ZJLyUubW92YWJsZWxpbWl0c0dGSS8lJ2FjY2VudEdGSS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVGLi1GIzYlLUY7NiRRIjJGJ0Y+RjJGNUZARkMtRkQ2LVEiLkYnRj5GRy9GS0ZJRkxGTkZQRlJGVEZWL0ZaRlgtRkQ2LVEifkYnRj5GR0Zgb0ZMRk5GUEZSRlRGVkZhby1GRDYtUSMuLkYnRj5GR0Zgb0ZMRk5GUEZSRlQvRldRLDAuMjIyMjIyMmVtRidGYW9GXW9GPg== there are, where 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 is the contribution which does not involve any parameter and 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 etc are the vector coefficients of the parameters. [See Maple soln worksheet for graphical representation.]solution1.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEmc29sdmVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GNjYmLUYjNiUtRiw2JVEiJUYnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZELyUlb3BlbkdRInxmckYnLyUmY2xvc2VHUSJ8aHJGJ0ZBRkRGREZBRkQ=a)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) From the tutor:
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 are the leading variables, 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 are the free variables.
c)
these are the leading variable eqns:
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
(the Maple Linear System Solving tutor chooses 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 forwards as in our scheme, rather than backwards as in the BackwardSubstitute command)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 result: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)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 REPRESENTATION (suppressing the last coordinate, ignoring LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUlYm9sZEdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtSSNtbkdGJDYmUSI0RidGMi8lJ2l0YWxpY0dGNC9GNlEnbm9ybWFsRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHUSMxMkYnRjJGPkZA)QyQtSSV3aXRoRzYiNiNJJnBsb3RzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlISIiNyY3JSIiKCIiJiIiISwmRiMiIiItSSIqRyUqcHJvdGVjdGVkRzYkJCIjOCEiIjclISIjRihGKEYoLChGI0YoRilGKC1GKjYkJCIjN0YvNyUiIiQhIiVGJkYoLCZGI0YoRjNGKA==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JSFHTTdSMApJNlJUQUJMRV9TQVZFLzE2NTYzMDA3MlgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIzAiJCImIiIjIiIkIiIiIiIlRidGKSIiIUYqRikiIzUhIiJGKSIjTSIjSiIjN0YlTTdSMApJNlJUQUJMRV9TQVZFLzQ1NDA4MDQwOFgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIzAiJCImIiIiIiIhRihGKEYnRigiIiMhIiJGKCEiJCIiJUYoIiIoIiImRihGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzQ1NDA4MDY5NlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiUiJSwoIiIoIiIiJiUkX3QwRzYjIiIjISIjJkYrNiNGKSIiJCwoIiImRilGKkYpRi8hIiVGKkYvRiU=TTdSMApJNlJUQUJMRV9TQVZFLzQ1NDE3ODMxMlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiUiJSwoIiIoIiIiJiUidEc2I0YpISIjJkYrNiMiIiMiIiQsKCIiJkYpRipGKUYuISIlRipGLkYl