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223midterm20081

# 223midterm20081 - University of Toronto Department of...

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University of Toronto Department of Mathematics MAT223H1S Linear Algebra I Midterm Examination February 28, 2008 W. Abou-Salem, A. Hammerlindl, D. Krepski, S. Uppal 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

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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) If the homogeneous system of linear equations A x = 0 has only the trivial solution, then A x = b has a unique solution for every vector b . true false [4] 1(b) If A and B are square matrices and both AB = 0 and BA = 0, then either A = 0 or B = 0. 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.

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