11:18 Done elementary_linear_algebra_8th_edi... O a S (if 26. Determine whether the set S = {-2x + x², 8 + x³, –x² + x³, -4 + x²} spans P3. Testing for Linear Independence In Exercises 27–40, determine whether the set S is linearly independent or linearly dependent. 6) 27. S = {(-2, 2), (3, 5)} 28. S = {(3, –6, (– 1, 2)} 5) 29. S = {(0, 0), (1, – 1)} 30. S = {(1, 0), (1, 1), (2, – 1)} = {(1, – 4, 1), (6, 3, 2)} = {(6, 2, 1), (– 1, 3, 2)} = {(-2, 1, 3), (2, 9, – 3), (2, 3, – 3)} 18) 31. S = 32. S 33. S 4. ") 34. S = {(1, 1, 1), (2, 2, 2), (3, 3, 3)} {(G, 1. ). (3, 4. 3). (–}, 6 2)} 36. S = {(-4, – 3, 4), (1, – 2, 3), (6, 0, 0)} 37. S = {(1, 0, 0), (0, 4, 0), (0, 0, –6), (1, 5, –3)} 38. S = {(4, –3, 6, 2), (1, 8, 3, 1), (3, – 2, – 1, 0)} 39. S = {(0, 0, 0, 1), (0, 0, 1, 1), (0, 1, 1, 1), (1, 1, 1, 1)} : {(4, 1, 2, 3), (3, 2, 1, 4), (1, 5, 5, 9), (1, 3, 9, 7)} 35. S = atrices linear 40. S = Testing for Linear Independence In Exercises 41–48, determine whether the set of vectors in P, is linearly independent or linearly dependent. hether n give s span. )} 41. S = {2 – x, 2x – x², 6 – 5x + x²} 42. S = {–1+ x², 5 + 2x} 43. S = {1 + 3x + x², – 1 + x + 2x², 4x} 44. S = {x², 1 + x²} 45. S = {-x + x², – 5 + x, –5 + x²} 46. S = {-2 – x, 2 + 3x + x², 6 + 5x + x²} 47. S = {7 – 3x + 4x², 6 + 2x – x², 1 – 8x + 5x²} 48. S = {7 – 4x + 4x², 6 + 2x – 3x², 20 – 6x + 5x²} Testing for Linear Independence In Exercises 49–52, determine whether the set of vectors in M2, is linearly independent or linearly dependent. hether en give s span. -2 49. A = B = -2 1 50. A = B = Г1 -11 Г 31 [ -81

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