Spring 2007 - Takeda's Class - Practice Exam 2

Spring 2007 - Takeda's Class - Practice Exam 2 - Math 20F,...

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Unformatted text preview: Math 20F, Practice Midterm 2 Solutions May 17, 2007 Name : PID : TA : Sec. No : Sec. Time : 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) Let T : R 2 R 2 be a linear transformation such that T ( e 1 ) = 2- 1 and T ( e 2 ) =- 1 2 . Find the matrix of the linear transformation T . Answer : 2- 1- 1 2 . (b) For the above T , is it 1-1? Justify your answer. Answer : It is 1-1. Justification: T is 1-1 iff the homogeneous system A x = has only the trivial solution. But since A is a square matrix, this happens iff A- 1 exists, i.e. det A 6 = 0. Now det A = 4- 1 = 3 6 = 0. 2 2. (a) Let A = - 1 2 4 2- 5- 5 3- 7- 8 ....
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Spring 2007 - Takeda's Class - Practice Exam 2 - Math 20F,...

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