Spring 2005 - Nagy's Class - Exam 1

Spring 2005 - Nagy's Class - Exam 1 - Math 20F Midterm Exam...

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Unformatted text preview: Math 20F Midterm Exam (version 1) April 29, 2005 1. (6 points) Consider the system x 1- 2 x 2 + 2 x 3 = 10 x 2 + 3 x 3 = 6 x 1- 3 x 2- x 3 = 4 . (a) Determine the solution set of the system and write it in parametric form. The augmented matrix is B = 1- 2 2 10 1 3 6 1- 3- 1 4 . The reduced echelon form of B is 1 8 22 1 3 6 . Thus, x 3 is free, x 1 =- 8 x 3 + 22, and x 2 =- 3 x 3 + 6. The parametric form of the solution set is x = t - 8- 3 1 + 22 6 , t any scalar . (b) The coefficient matrix for the above system is A = 1- 2 2 1 3 1- 3- 1 . Are the columns of A linearly independent or linearly dependent? Justify your answer. The columns of A are linearly dependent since the reduced echelon form of A has a zero row and therefore the homogeneous equation A x = has nontrivial solutions. In fact, 8 1 1 + 3 - 2 1- 3 - 2 3- 1 = is a typical dependence relation.is a typical dependence relation....
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Spring 2005 - Nagy's Class - Exam 1 - Math 20F Midterm Exam...

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