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Spring 2007 - Takeda's Class - Exam 1

# Spring 2007 - Takeda's Class - Exam 1 - Math 20F Midterm 1...

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Math 20F, Midterm 1 Solutions April 23, 2007 Name: Section: This exam consists of 7 pages including this front page. Ground Rules 1. No calculator is allowed. 2. Show your work for every problem. A correct answer without any justification will receive no credit. 3. You may use one 4-by-6 index card, both sides. 4. Show your ID on your desk. Score 1 10 2 10 3 10 4 10 5 10 6 10 Total 60 1

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1. (a) Reduce the matrix - 2 1 3 1 6 - 3 - 9 2 to the reduced echelon form. Answer : - 2 1 3 1 6 - 3 - 9 2 - 2 1 3 1 0 0 0 5 - 2 1 3 1 0 0 0 1 - 2 1 3 0 0 0 0 1 1 - 1 2 - 3 2 0 0 0 0 1 . (b) If the above matrix corresponds to the augmented matrix of a system of linear equations, then how many solutions are there? Answer : The system is inconsistent, i.e. there is no solution. 2
2. Let A = - 5 6 12 - 2 2 4 2 - 1 - 2 and b = 1 - 2 h . Chose h so that the system A x = b is consistent. Answer : Consider - 5 6 12 1 - 2 2 4 - 2 2 - 1 - 2 h - 2 2 4 - 2 - 5 6 12 1 2 - 1 - 2 h 1 - 1 - 2 1 - 5 6 12 1 2 - 1 - 2 h 1 - 1 - 2 1 0 1 2 6 0 1 2 h - 2

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Spring 2007 - Takeda's Class - Exam 1 - Math 20F Midterm 1...

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