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Suppose four polynomials p1 ,p2 ,p3 ,q in P2 have augmented matrix A corresponding to the equation above has echelon form Are the three polynomials

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Suppose four polynomials p1 ,p2 ,p3 ,q in P2 have augmented matrix A corresponding to the equation above has echelon form Are the three polynomials 391, 192, p3 linearly independent? {Yes/No) \fGive the correct reason from Your response Correct response There are non-leading columns in the first 3 columns of U If they are linearly dependent, then give a linear combination of p1 and p2 which equals P3 . If they are linearly independent, then give a linear combination of p1 , p2 and p3 which equals q. Write the linear combination only -- there should be no equals sign. Use p1, p2, p3 for the polynomials P1 , P2, P3 and use an asterisk * for scalar multiplication. For example, a typical answer might look like this: 3*p1 + 2*p2 Your response Correct response No answer 7*p2-17*p1

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