# Matrices and Their Roots: A Textbook of Matrix Algebra/With by A. R. Heesterman

By A. R. Heesterman

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Additional resources for Matrices and Their Roots: A Textbook of Matrix Algebra/With Disk

Example text

A) 6 12x (B) 10x3 24x 3 ANSWERS (C) 1x ϩ 2 21x ϩ 3 (D) 1 3 1Ϫ 2 y TO MATCHED PROBLEMS 5 9 9 5 1. (A) 2 u (B) 2 (6x2y5)2 or (2 6x2y5)2 (C) 1 ր 2 (3xy)3 4ր7 3 3 1ր3 (E) Ϫ(2x) (F) (x ϩ y ) 3 2 3 2 2. (A) u2 ϩ v2 (B) 213 (C) (2 x ) ր2 or 12 2 x 3. (A) 3x2yz 12xz (B) 3a2b2b2 ϭ 3a2b1b (C) 22x2y 5 3 2 3 2 4. (A) 8 12 (B) Ϫ522x y (C) 32mn ϩ 41mn 5. (A) 3 12 Ϫ 413 (B) 213 Ϫ 5 (C) y ϩ 21y Ϫ 8 4 3 2 3 (D) x ϩ 2 xyϪ 2 xy2 Ϫ y 312x 3 6. (A) (B) 5x2 2 2x2 x R-3 In Problems 1–8, change to radical form. Do not simplify.

100 Ϭ 0 16. 0 Ϭ 0 17. 0 Ϭ (9 ؒ 8) 18. 19. 0 ؒ a100 ϩ 1 b 100 4 6 Ϭ a3 Ϫ b 7 2 20. 3(0 ϩ 5) Ϭ 204 Ϫ1 11 bar67388_chR_001-013 12 11/02/06 00:50 CHAPTER R Page 12 BASIC ALGEBRAIC OPERATIONS In Problems 21–26, perform the indicated operations and express the result in the form a͞b, where a and b are integers. 4 12 21. ϩ 9 5 23. Ϫa 4 1 ϩ b 100 25 3 Ϫ1 25. a b ϩ 2Ϫ1 8 17 2 22. ؒ 8 7 50. Indicate which of the following are true: (A) All integers are natural numbers. (B) All rational numbers are real numbers.

2 Ϫ8 3 16. 2 Ϫ27 17. Ϫ1128 18. Ϫ 1125 19. 127 Ϫ 5 13 20. 218 ϩ 118 3 3 3 21. 2 5Ϫ 2 25 ϩ 2 625 3 3 22. 220 ϩ 2 40 Ϫ 2 5 3 3 23. 2 25 2 10 24. 16114 25. 29x8y4 26. 216m4y8 4 27. 216m4n8 5 28. 232a15b10 4 29. 2 m2 10 6 30. ͙ n 5 3 31. 2 1 xy 4 32. 2 15x 3 3 33. 29x2 29x 34. 12x18xy In Problems 35–46, rationalize denominators, and write in simplified form. 35. 38. 1 215 10 25 4 36. 1 317 37. 39. 2 144 40. 41. 6x 13x 42. 44. 4 16 Ϫ 2 45. 12y 2 16y 12 16 ϩ 2 1 17 3 3 254 3 43. 2 12 Ϫ 1 46. 12 110 Ϫ 2 In Problems 47–54, write in simplified form.