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223final20079

# 223final20079 - Faculty of Arts and Science University of...

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Faculty of Arts and Science University of Toronto Final Examination , December 2007 MAT223H1F Linear Algebra I P. Bachurin, A. Fischer, B. Koenig, 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 /8 2 /8 3 /12 4 /10 5 /10 6 /12 7 /10 8 /10 TOTAL /80 1 of 13

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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) The standard basis { ± 1 0 ² , ± 0 1 ² } is the only orthonormal basis for R 2 . true false [4] 1(b) There is a linear transformation L : R 3 7→ R 3 such that the range of L equals the kernel of L . true false 2 of 13
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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223final20079 - Faculty of Arts and Science University of...

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