223final20061 - Faculty of Arts and Science University of...

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Faculty of Arts and Science University of Toronto Final Examination , April/May 2006 MAT223H1S Linear Algebra I J. Adler, A. Esterov, V. Jurdjevic, S. Uppal Duration: 3 hours Last Name: Given Name: Student Number: No calculators or other aids are allowed. FOR MARKER USE ONLY Question Mark 1 /10 2 /10 3 /10 4 /10 5 /14 6 /10 7 /8 8 /8 TOTAL /80 1 of 14
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Indicate your answer for the true/false questions by shading in the box corre- sponding to your choice. Each correct answer is worth 2 marks . [10] 1. Determine if the following statements are guaranteed to be true. (a) The set of solutions of each system of linear equations in n unknown variables is a sub- space of R n . true false (b) If V is a finite dimensional vector space and W is s subspace of V then dim ( W ) dim ( V ). true false (c) If U and W are subspaces of a vector space V then the set of vectors that belong to either U or W is a subspace of V . true false (d) W = { ( x, y, z ) R 3 | ( x + y + z ) 2 = 0 } is a subpsace of
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223final20061 - Faculty of Arts and Science University of...

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