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# assignment1 - c 1 1 3 1 2 1 1 2 2 3 2 2 2 1 3 2 1 1 1 1 1 n...

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University of Toronto at Scarborough Department of Computer and Mathematical Sciences Linear Algebra II MATB24 Fall 2010 Assignment # 1 You are expected to work on this assignment prior to your tutorial in the week of September 20th, 2008. You may ask questions about this assignment in that tutorial. In your tutorial in the week of September 27th 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 1 Section 4 and 5, Chapter 4 section 2 and week 1 Lecture Notes Problems: 1. , Pages 69 -70 # 23, 24, 29, 40, 41, 42, 43 2. , Pages 84-85 # 7, 8, 19 3. , Pages 261 -262 # 8, 29 4. Addition: 1) Calculate: a) 1 2 3 4 5 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 a x a x a x a x a x b) 3 3 2 3 1 3 3 2 2 2 1 2 3 1 2 1 1 1 1 1 1 1 1 1 1 1 1 y x y x y x y x y x y x y x y x y x

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Unformatted text preview: c) 1 1 3 1 2 1 1 2 2 3 2 2 2 1 3 2 1 1 1 1 1 n n n n n n n x x x x x x x x x x x x 2) Discuss the constants a , b , c so that the following system has trivial solution 2 2 2 z c cy x z b by x z a ay x 3) Show that Z 7 is a field. Show that Z 6 is not a field. 4) 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 . 5) Is the matrix A = 3 4 6 5 over Z 7 invertible? Where isn’t A invertible over? Note: There are answers at the back of the textbook for the odd number questions....
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assignment1 - c 1 1 3 1 2 1 1 2 2 3 2 2 2 1 3 2 1 1 1 1 1 n...

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