By Genov G.K.
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Extra resources for A basis of identities of the algebra of third-order matrices over a finite field
Communicate with your employer and family members the importance of your success in this course so that they can support you. • Be sure to find out the type of calculator (if any) that your instructor requires. Also determine if there will be online homework or other computer requirements. 2. During the Course • To prepare yourself for the next day’s class, read the section in the text before coming to class. This will help you familiarize yourself with the material and terminology. • Attend every class, and be on time.
Qxd 7/14/09 10:28 AM Page 14 INTERM— 14 Chapter R Review of Basic Algebraic Concepts 11. Check the sets to which each number belongs. 2 12. Check the sets to which each number belongs. 2 Concept 2: Inequalities For Exercises 13–20, fill in the blanks with the appropriate symbol: 6 or 7. 13. Ϫ9 ___ Ϫ1 17. 14. 0 ___ Ϫ6 5 10 ___ 3 7 18. ) 15. 15 16. 5 5 1 19. Ϫ ___ Ϫ 8 8 20. Ϫ 13 17 ___ Ϫ 15 12 Concept 3: Interval Notation For Exercises 21–28, express the set in interval notation. 21. 22. ( 25. 9 26.
3, Ϫ2, Ϫ1, 0, 1, 2, 3, . . }. The set of rational numbers consists of all the numbers that can be defined as a ratio of two integers. 2 Sets of Numbers and Interval Notation DEFINITION Rational Numbers The set of rational numbers is 5 q 0 p and q are integers and q does not equal zero}. p Example 1 Identifying Rational Numbers Show that each number is a rational number by finding two integers whose ratio equals the given number. a. Ϫ4 7 b. 8 c. 6 d. 87 Solution: a. Ϫ4 7 is a rational number because it can be expressed as the ratio of the integers Ϫ4 and 7.
A basis of identities of the algebra of third-order matrices over a finite field by Genov G.K.