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Spring 2007 - Takeda's Class - Practice Exam 1

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

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Unformatted text preview: Math 20F, Practice Midterm 1 Solutions April 22, 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 1. (a) Reduce the matrix 1 3- 5 2 6- 15 2 to the reduced echelon form. Answer : 1 3- 5 2 6- 15 2 ∼ 1 3- 5 0 0 0- 5 2 ∼ 1 3- 5 0 0 1- 2 5 ∼ 1 3 0- 2 0 0 1- 2 5 (b) If the above matrix corresponds to the augmented matrix of a system of linear equations, then how many solutions are there? Answer : There are infinitely many solutions. 2 2. Let A = 1- 4 3- 1- 2 6 3 and b = 4 1- 4 . Denote the columns of A by a 1 , a 2 , and a 3 . Is b in Span { a 1 , a 2 , a 3 } ? Justify your answer....
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Spring 2007 - Takeda's Class - Practice Exam 1 - Math 20F...

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