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In Exercises 24–29, solve by Cramer’s rule, where it applies.
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Elementary Linear Algebra: Applications Version
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- Classify the quadratic forms in Exercises 9–18. Then make a change of variable, x = Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. Construct P using the methods of Section 7.1. 11. 2x² + 10x1x2 + 2x3arrow_forwardExercises 38–40 will help you prepare for the material covered in the first section of the next chapter. In Exercises 38-39, simplify each algebraic expression. 38. (-9x³ + 7x? - 5x + 3) + (13x + 2r? – &x – 6) 39. (7x3 – 8x? + 9x – 6) – (2x – 6x? – 3x + 9) 40. The figures show the graphs of two functions. y y 201 10- .... -20- flx) = x³ glx) = -0.3x + 4x + 2arrow_forwardExercises 99–108: Solve the given equation for the specified variable. 101. P = 2L + 2W for Larrow_forward
- In Exercises 20–21, solve each rational equation. 11 20. x + 4 + 2 x2 – 16 - x + 1 21. x? + 2x – 3 1 1 x + 3 x - 1 ||arrow_forwardIn Exercises 59–64, solve and check each linear equation. 59. 2x – 5 = 7 60. 5x + 20 = 3x 61. 7(x – 4) = x + 2 62. 1 - 2(6 – x) = 3x + 2 63. 2(x – 4) + 3(x + 5) = 2x – 2 64. 2x 4(5x + 1) = 3x + 17arrow_forwardFor Exercises 5–10, a. Simplify the expression. b. Substitute 0 for h in the simplified expression. 2(x + h)? + 3(x + h) · 5. (2x + 3x) 3(x + h - 4(x + h) – (3x - 4x) 6. h 1 1 1 1 (x + h) – 2 7. x - 2 2(x + h) + 5 8. 2x + 5 h (x + h) – x 9. (x + h) 10. - X h harrow_forward
- For Exercises 101–104, verify by substitution that the given values of x are solutions to the given equation. 101. x + 25 = 0 102. x + 49 = 0 a. x = 5i a. x = 7i b. x = -5i b. x = -7i 103. x - 4x + 7 = 0 104. x - 6x + 11 = 0 a. x = 2 + iV3 b. x = 2 – iV3 a. x = 3 + iVā b. x = 3 – iV2arrow_forwardExercises 43–52: Complete the following. (a) Solve the equation symbolically. (b) Classify the equation as a contradiction, an identity, or a conditional equation. 43. 5x - 1 = 5x + 4 44. 7- 9: = 2(3 – 42) – z 45. 3(x - 1) = 5 46. 22 = -2(2x + 1.4) 47. 0.5(x – 2) + 5 = 0.5x + 4 48. 눈x-2(x-1)3-x + 2 2x + 1 2x 49. 50. x – 1.5 2- 3r - 1.5 51. -6 52. 0.5 (3x - 1) + 0.5x = 2x – 0.5arrow_forwardExercises 7–12: Determine whether the equation is linear or nonlinear by trying to write it in the form ax + b = 0. 7. 3x – 1.5 = 7arrow_forward
- For the functions in Exercises 39–42,arrow_forwardFor Exercises 19–26, simplify each expression and write the result in standard form, a + bi. 8 + 3i 19. 4 + 5i 20. -4 - 6i 21. 9 - 15i 22. 14 6. -2 -3 -18 + V-48 23. - 20 + V-50 14 - V-98 25. - 10 + V-125 24. 26. 4 10 -7arrow_forwardFor Exercises 39–42, multiply the radicals and simplify. Assume that all variable expressions represent positive real numbers. 39. (6V5 – 2V3)(2V3 + 5V3) 40. (7V2 – 2VIT)(7V2 + 2V1T) 41. (2c²Va – 5ď Vc) 42. (Vx + 2 + 4)²arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage