hw1 - + a b a a b b b a a b a a a b a b (1) Prove that S a...

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MATH 4377, ADVANCED LINEAR ALGEBRA, SUMMER 2011, HW#1 Due date: Tuesday, June 7th Remark : In order to do this set of hw, you may need to read the Appendics about the definition of the fields. 1. Recall that complex numbers are of the form x = a + bi with a,b are (arbitrary) real numbers and i = - 1 (i.e. i 2 = - 1). Let C be the set of complex numbers. (a) Show that C (with the standard addition and multiplication) is field by verifying F1-F5 on Page 553. (b) Let x = 3 + 5 i . Find x - 1 . 2. Let S = { a,b } . Define the addition “+” and multiplication “ · ” on S by the following charts:
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Unformatted text preview: + a b a a b b b a a b a a a b a b (1) Prove that S a eld under the the addition + and multiplication dened above by verifying F1-F5 on Page 553. (2) Identify the elements of S that are 0, 1 and -1. 3. Let F be the set of all polynomials. Is F a eld with the standard addition and multiplication? State your reason. 4. Probelm 13 on Page 15. 5. Probelm 18 on Page 15. 6. Problem 21 on Page 16. 7. Problem 8 (b), (d) and (f) on Page 20. 1...
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