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e207k

# e207k - MAS 3105 Feb 1 2007 Quiz 2 and Key Prof S Hudson...

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Unformatted text preview: MAS 3105 Feb 1, 2007 Quiz 2 and Key Prof. S. Hudson 1) [20pt] Find the determinants of these two matrices. If possible, find quick ways to do them (without using the definition) and explain briefly. Hint for A : if you swap two rows, the matrix becomes upper triangular. A = 1 2 3 4 6 5 5 6 7 4 B = 1 2 4 2 4 8 4 8 16 2) [20pt] Solve for X given that AX + B = X and A = 1- 1 B =- 2- 2 6 8 3) [20pt] Choose ONE of these to prove. You can answer on the back. a) If A is nonsingular then it is row equivalent to A- 1 . [You can quote theorems or results from HW to give a very short proof] b) Prove this part of Thm 1.4.2: If A is row equivalent to I , then A is nonsingular. Remarks and Answers: The average score was 16+7+10=33 out of 60, which is pretty low for Quiz 2. Problem 2 was based on HW from Ch 1.3, and should have been pretty easy. Also, you should walk into each quiz ready for any advertised proofs such as Problem 3b), [Thm 1.4.2]....
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e207k - MAS 3105 Feb 1 2007 Quiz 2 and Key Prof S Hudson...

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