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Unformatted text preview: Math 20F, Midterm 2 May 21, 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 4by6 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 A = 1 1 1 1 . Find Nul A . Answer : Consider the homogeneous system A x = , namely 1 1 0 1 1 0 ∼ 1 1 0 0 0 0 . So x 1 + x 2 = 0, i.e. x 2 = x 1 . So the solutions are x 1 x 2 = x 2 1 1 . Hence Nul A = Span { 1 1 } . (b) For the above A , is the corresponding linear transformation onto? Jus tify your answer. Answer : For a square matrix, the corresponding linear transformation is onto if and only if it is invertible. But det A = 1 · 1 1 · 1 = 0 . So it is not onto. 2 2. (a) Let A = 1 2 4 5 0 1 5 6 0 0 1 9 0 0 1 ....
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 Spring '03
 BUSS
 Math, Linear Algebra, Algebra, Vector Space, TA, linear transformation

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