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# assignment1 - Problems 1 Fraleigh& Beauregard...

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University of Toronto at Scarborough Department of Computer and Mathematical Sciences Linear Algebra II MATB24 Fall 2008 Assignment # 1 You are expected to work on this assignment prior to your tutorial in the week of September 15th, 2008. You may ask questions about this assignment in that tutorial. In your tutorial in the week of September 22nd you will be asked to write a quiz based on this assignment and/or related material from the lectures and tutorials in week 1 and textbook readings. Textbook: Linear Algebra by Fraleigh & Beauregard, 3rd edition. Read: Chapter 3 Section 1 and Lecture 1 Notes
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Unformatted text preview: Problems: 1. Fraleigh & Beauregard , Pages189-190 # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 18, 19, 22, 23, 24, 25. 2. Addition: 1) Show that Z 5 is a field. Show that Z 6 is not a field. 2) Determine if that U = { 3 b a + | a , b ∈ Q} is a field under the operations ⊕ and ⊗ , where is given by ( ⊕ 3 b a + ) ⊕ ( 3 d c + ) = 3 ) ( ) ( d b c a + + + and ⊗ is given by ( 3 b a + ) ⊗ ( 3 d c + ) = 3 ) ( ) 3 ( bc ad bd ac + + + . 3) Is the matrix A = over Z 7 invertible? ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ 3 4 6 5 Note: There are answers at the back of the textbook for the odd number questions....
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