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math111hw5 - MATH111 HW 5 Due Date 15th Oct 2007(Mon Please...

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MATH111 HW 5 Due Date: 15th, Oct, 2007 (Mon) Please hand in your homework in the tutorial session or by putting it in the collection box outside MATH dept (Rm 3461, Lift 25-26). Ch 3.2 # 10 Find the following determinant by row reduction to echelon form. 1 3 - 1 0 - 2 0 2 - 4 - 1 - 6 - 2 - 6 2 3 9 3 7 - 3 8 - 7 3 5 5 2 7 Ch 3.2 # 18 Find the following determinant where a b c d e f g h i = 7. g h i a b c d e f Ch 3.2 # 20 Find the following determinant where a b c d e f g h i = 7. a + d b + e c + f d e f g h i Ch 3.2 # 26 Use determinants to decide if the following set of vectors is linearly inde- pendent. 3 5 - 6 4 , 2 - 6 0 7 , - 2 - 1 3 0 , 0 0 0 3 Ch 3.2 # 28 In the following, A and B are n × n matrices. Mark each statement True or False. Justify each answer. a. If two row interchanges are made in succession, then the new deter- minant equals the old determinant. b. The determinant of A is the product of the diagonal entries in A .
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