Assignment 1 - of Z 5 . 2. (a) Give the addition and...

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University of Toronto at Scarborough MAT B24S Fall 2007 Assignment #1 You are expected to work on this assignment prior to your tutorial in the week of September 17. You may ask questions about this assignment in that tutorial. In your tutorial in the week of September 24 you will be asked to write a quiz based on this assignment and/or related material from the lectures and textbook readings. TEXTBOOK: Linear Algebra, 3rd edition Fraleigh Beauregard READ: Lectures 1 and 2 Notes. Section 3.1 PROBLEMS: 1. (a) Give the addition and multiplication tables for Z 5 with the usual addition and multiplication as defined in class. (b) Is Z 5 with the usual addition and multiplication a field? If your answer is yes then: i). Find the additive inverses of each element of Z 5 . ii). Find the multiplicative inverses of each nonnegative element
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Unformatted text preview: of Z 5 . 2. (a) Give the addition and multiplication tables for Z 9 with the usual addition and multiplication as defined in class. i). Is Z 9 with the usual addition and multiplication a field? If your answer is yes, then: ii). Find the additive inverses of each element of Z 9 . iii). Find the multiplicative inverses of each nonnegative element of Z 9 . 3. Is the set M 2x2 of all 2 x 2 invertible matrices, with the usual matrix addition and multiplication a field? Justify your answer. 4. Is the set Q [ √ 7] = { a + b √ 7 | a, b ∈ Q } with addition and multiplication defined by: ( a + b √ 7) ⊕ ( c + d √ 7) = ( a + c ) + ( b + d ) √ 7 for all a, b, c, d ∈ Q ( a + b √ 7) ⊗ ( c + d √ 7) = ( ac + 7 bd ) + ( ad + bc ) √ 7 for all a, b, c, d ∈ Q a field? 5. Section 3 . 1 : #2 , 6 , 14 , 18...
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This note was uploaded on 12/20/2010 for the course MAT MATB24 taught by Professor X.jiang during the Spring '10 term at University of Toronto.

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Assignment 1 - of Z 5 . 2. (a) Give the addition and...

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