223final20081 - Faculty of Arts and Science University of Toronto Final Examination April/May 2008 MAT223H1S Linear Algebra I W Abou-Salem A

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Unformatted text preview: Faculty of Arts and Science University of Toronto Final Examination , April/May 2008 MAT223H1S Linear Algebra I W. Abou-Salem, A. Hammerlindl, D. Krepski, 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 /12 6 /10 7 /10 8 /10 TOTAL /80 1 of 14 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 { u, v } is an orthonormal set in R 3 , then { u, v, u × v } is an orthonormal basis of R 3 . true false [4] 1(b) If V is a finite dimensional vector space, then every linear transformation L : V → V that is one-to-one is also onto. true false 2 of 14 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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This note was uploaded on 01/19/2010 for the course MAT MAT223 taught by Professor Uppal during the Spring '09 term at University of Toronto- Toronto.

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223final20081 - Faculty of Arts and Science University of Toronto Final Examination April/May 2008 MAT223H1S Linear Algebra I W Abou-Salem A

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