compute A=AA, AAAA, and A+. Describe the pattern that emerges, and use this pattern to find...

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compute A²=AA, AAAA, and A+. Describe the pattern that emerges, and use this pattern to find A 1001. Interpret your answers geometrically, in terms of rotations, reflections, shears, and orthogonal projections. 33. 34. 36. 37. 39. 40. 35. 38. 12 [ 41. 42. In Exercises 43 through 48, find a 2 x 2 matrix A with the given properties. Hint: It helps to think of geometrical examples. 43. A 12. A² = 12 45. A² 12. A³ = 12 44. A² 12. A = 12 46. A2A, all entries of A are nonzero. 47. AA, all entries of A are nonzero. 48. A 10 11 compute A²=AA, AAAA, and A+. Describe the pattern that emerges, and use this pattern to find A 1001. Interpret your answers geometrically, in terms of rotations, reflections, shears, and orthogonal projections. 33. 34. 36. 37. 39. 40. 35. 38. 12 [ 41. 42. In Exercises 43 through 48, find a 2 x 2 matrix A with the given properties. Hint: It helps to think of geometrical examples. 43. A 12. A² = 12 45. A² 12. A³ = 12 44. A² 12. A = 12 46. A2A, all entries of A are nonzero. 47. AA, all entries of A are nonzero. 48. A 10 11

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