223midterm20089 - University of Toronto Department of...

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Unformatted text preview: University of Toronto Department of Mathematics MAT223H1F Linear Algebra I Midterm Examination October 23, 2008 G. Gotsbacher, B. Jacob, S. Uppal, F. Ziltener Duration: 1 hour 50 minutes Last Name: Given Name: Student Number: Tutorial Code: No calculators or other aids are allowed. FOR MARKER USE ONLY Question Mark 1 /8 2 /8 3 /8 4 /10 5 /10 6 /10 7 /6 TOTAL /60 1 of 8 For each of the statements below, decide if it is true or false. Indicate your answer by shading in the box corresponding to your choice. Justify your answer by providing an appropriate proof or counter example. [4] 1(a) The set S = { ( x, y ) R 2 | xy = 0 } is a vector subspace of R 2 . true false [4] 1(b) The set S = { (1 , , , 0) , (0 , 1 , 1 , 0) , (0 , , 1 , 1) , (1 , , , 1) , (- 1 , 1 , 2 , 1) } spans R 4 . true false 2 of 8 For each of the statements below, decide if it is true or false. Indicate your answer by shading in the box corresponding to your choice. Justify your answer by providing an appropriate proof or counter example.by providing an appropriate proof or counter example....
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223midterm20089 - University of Toronto Department of...

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