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解线性方程组 by Juan Carlos Ponce Campuzano

解线性方程组 by Juan Carlos Ponce Campuzano
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2017-03-06 12:05
函数解析几何几何作图
该范例演示了解线性方程组的过程。涉及的核心数学概念包括线性方程组的解法。通过使用 GeoGebra 命令如 Segment, If, Length, Sequence, Circle, Sum 等，可以构造出线性方程组的几何表示。适合高中数学教学和学习使用。

GeoGebra 命令及参数

  1. Segment(C1, C2) → E2
  2. Segment(C1, C3) → E1
  3. Segment(C3, C2) → E3
  4. Segment(C4, C2) → E5
  5. Segment(C3, C4) → E4
  6. Segment(C4, C5) → E6
  7. Segment(C5, C6) → E8
  8. Segment(C5, C7) → E7
  9. Segment(C6, C7) → E9
  10. Segment(C6, C8) → E11
  11. Segment(C7, C8) → E10
  12. Segment(C8, C9) → E12
  13. Segment(C9, C10) → E15
  14. Segment(C10, C11) → E16
  15. Segment(C10, C12) → E18
  16. Segment(C11, C12) → E17
  17. Segment(C12, C13) → E19
  18. Segment(C14, C1) → E23
  19. Segment(C13, C14) → E20
  20. Segment(C13, C15) → E21
  21. Segment(C14, C15) → E22
  22. If(level ≟ true, Segment[C9, C1], Segment[C1, C15]) → E14
  23. If(level ≟ true, Segment[C9, C2], Segment[C9, C11]) → E13
  24. If(level ≟ false, {E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, E17, E18, E19, E20, E21, E22, E23}, {E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14}) → list1
  25. Length(list1) → numb
  26. Sequence(Intersect[E1, Element[list1, i]], i, 1, numb) → F1
  27. Circle((0, 0), 1) → c
  28. Sequence(Intersect[E2, Element[list1, i]], i, 1, numb) → F2
  29. Sequence(Intersect[E3, Element[list1, i]], i, 1, numb) → F3
  30. Sequence(Intersect[E4, Element[list1, i]], i, 1, numb) → F4
  31. Sequence(Intersect[E5, Element[list1, i]], i, 1, numb) → F5
  32. Sequence(Intersect[E6, Element[list1, i]], i, 1, numb) → F6
  33. Sequence(Intersect[E7, Element[list1, i]], i, 1, numb) → F7
  34. Sequence(Intersect[E8, Element[list1, i]], i, 1, numb) → F8
  35. Sequence(Intersect[E9, Element[list1, i]], i, 1, numb) → F9
  36. Sequence(Intersect[E10, Element[list1, i]], i, 1, numb) → F10
  37. Sequence(Intersect[E11, Element[list1, i]], i, 1, numb) → F11
  38. Sequence(Intersect[E12, Element[list1, i]], i, 1, numb) → F12
  39. Sequence(Intersect[E13, Element[list1, i]], i, 1, numb) → F13
  40. Sequence(Intersect[E14, Element[list1, i]], i, 1, numb) → F14
  41. Sequence(Intersect[E15, Element[list1, i]], i, 1, numb) → F15
  42. Sequence(Intersect[E16, Element[list1, i]], i, 1, numb) → F16
  43. Sequence(Intersect[E17, Element[list1, i]], i, 1, numb) → F17
  44. Sequence(Intersect[E18, Element[list1, i]], i, 1, numb) → F18
  45. Sequence(Intersect[E19, Element[list1, i]], i, 1, numb) → F19
  46. Sequence(Intersect[E20, Element[list1, i]], i, 1, numb) → F20
  47. Sequence(Intersect[E21, Element[list1, i]], i, 1, numb) → F21
  48. Sequence(Intersect[E22, Element[list1, i]], i, 1, numb) → F22
  49. Sequence(Intersect[E23, Element[list1, i]], i, 1, numb) → F23
  50. Sequence(If[Element[F1, i] ≠ Element[F1, i], (0, 0), Element[F1, i]], i, 1, numb) → G1
  51. Sequence(If[Element[F2, i] ≠ Element[F2, i], (0, 0), Element[F2, i]], i, 1, numb) → G2
  52. Sequence(If[Element[F3, i] ≠ Element[F3, i], (0, 0), Element[F3, i]], i, 1, numb) → G3
  53. Sequence(If[Element[F4, i] ≠ Element[F4, i], (0, 0), Element[F4, i]], i, 1, numb) → G4
  54. Sequence(If[Element[F5, i] ≠ Element[F5, i], (0, 0), Element[F5, i]], i, 1, numb) → G5
  55. Sequence(If[Element[F6, i] ≠ Element[F6, i], (0, 0), Element[F6, i]], i, 1, numb) → G6
  56. Sequence(If[Element[F7, i] ≠ Element[F7, i], (0, 0), Element[F7, i]], i, 1, numb) → G7
  57. Sequence(If[Element[F8, i] ≠ Element[F8, i], (0, 0), Element[F8, i]], i, 1, numb) → G8
  58. Sequence(If[Element[F9, i] ≠ Element[F9, i], (0, 0), Element[F9, i]], i, 1, numb) → G9
  59. Sequence(If[Element[F10, i] ≠ Element[F10, i], (0, 0), Element[F10, i]], i, 1, numb) → G10
  60. Sequence(If[Element[F11, i] ≠ Element[F11, i], (0, 0), Element[F11, i]], i, 1, numb) → G11
  61. Sequence(If[Element[F12, i] ≠ Element[F12, i], (0, 0), Element[F12, i]], i, 1, numb) → G12
  62. Sequence(If[Element[F13, i] ≠ Element[F13, i], (0, 0), Element[F13, i]], i, 1, numb) → G13
  63. Sequence(If[Element[F14, i] ≠ Element[F14, i], (0, 0), Element[F14, i]], i, 1, numb) → G14
  64. Sequence(If[Element[F15, i] ≠ Element[F15, i], (0, 0), Element[F15, i]], i, 1, numb) → G15
  65. Sequence(If[Element[G1, i] ≟ (0, 0), 1, 0], i, 1, numb) → H1
  66. Sequence(If[Element[G2, i] ≟ (0, 0), 1, 0], i, 1, numb) → H2
  67. Sequence(If[Element[G3, i] ≟ (0, 0), 1, 0], i, 1, numb) → H3
  68. Sequence(If[Element[G4, i] ≟ (0, 0), 1, 0], i, 1, numb) → H4
  69. Sequence(If[Element[G5, i] ≟ (0, 0), 1, 0], i, 1, numb) → H5
  70. Sequence(If[Element[G6, i] ≟ (0, 0), 1, 0], i, 1, numb) → H6
  71. Sequence(If[Element[G7, i] ≟ (0, 0), 1, 0], i, 1, numb) → H7
  72. Sequence(If[Element[G8, i] ≟ (0, 0), 1, 0], i, 1, numb) → H8
  73. Sequence(If[Element[G9, i] ≟ (0, 0), 1, 0], i, 1, numb) → H9
  74. Sequence(If[Element[G10, i] ≟ (0, 0), 1, 0], i, 1, numb) → H10
  75. Sequence(If[Element[G11, i] ≟ (0, 0), 1, 0], i, 1, numb) → H11
  76. Sequence(If[Element[G12, i] ≟ (0, 0), 1, 0], i, 1, numb) → H12
  77. Sequence(If[Element[G13, i] ≟ (0, 0), 1, 0], i, 1, numb) → H13
  78. Sequence(If[Element[G14, i] ≟ (0, 0), 1, 0], i, 1, numb) → H14
  79. Sequence(If[Element[G15, i] ≟ (0, 0), 1, 0], i, 1, numb) → H15
  80. Sequence(If[Element[F16, i] ≠ Element[F16, i], (0, 0), Element[F16, i]], i, 1, numb) → G16
  81. Sequence(If[Element[F17, i] ≠ Element[F17, i], (0, 0), Element[F17, i]], i, 1, numb) → G17
  82. Sequence(If[Element[F18, i] ≠ Element[F18, i], (0, 0), Element[F18, i]], i, 1, numb) → G18
  83. Sequence(If[Element[F19, i] ≠ Element[F19, i], (0, 0), Element[F19, i]], i, 1, numb) → G19
  84. Sequence(If[Element[F20, i] ≠ Element[F20, i], (0, 0), Element[F20, i]], i, 1, numb) → G20
  85. Sequence(If[Element[F21, i] ≠ Element[F21, i], (0, 0), Element[F21, i]], i, 1, numb) → G21
  86. Sequence(If[Element[F22, i] ≠ Element[F22, i], (0, 0), Element[F22, i]], i, 1, numb) → G22
  87. Sequence(If[Element[F23, i] ≠ Element[F23, i], (0, 0), Element[F23, i]], i, 1, numb) → G23
  88. Sequence(If[Element[G16, i] ≟ (0, 0), 1, 0], i, 1, numb) → H16
  89. Sequence(If[Element[G17, i] ≟ (0, 0), 1, 0], i, 1, numb) → H17
  90. Sequence(If[Element[G18, i] ≟ (0, 0), 1, 0], i, 1, numb) → H18
  91. Sequence(If[Element[G19, i] ≟ (0, 0), 1, 0], i, 1, numb) → H19
  92. Sequence(If[Element[G20, i] ≟ (0, 0), 1, 0], i, 1, numb) → H20
  93. Sequence(If[Element[G21, i] ≟ (0, 0), 1, 0], i, 1, numb) → H21
  94. Sequence(If[Element[G22, i] ≟ (0, 0), 1, 0], i, 1, numb) → H22
  95. Sequence(If[Element[G23, i] ≟ (0, 0), 1, 0], i, 1, numb) → H23
  96. Sum(H1) → I1
  97. Sum(H2) → I2
  98. Sum(H3) → I3
  99. Sum(H4) → I4
  100. Sum(H5) → I5
  101. Sum(H6) → I6
  102. Sum(H7) → I7
  103. Sum(H8) → I8
  104. Sum(H9) → I9
  105. Sum(H10) → I10
  106. Sum(H11) → I11
  107. Sum(H12) → I12
  108. Sum(H13) → I13
  109. Sum(H14) → I14
  110. Sum(H15) → I15
  111. Sum(H16) → I16
  112. Sum(H17) → I17
  113. Sum(H18) → I18
  114. Sum(H19) → I19
  115. Sum(H20) → I20
  116. Sum(H21) → I21
  117. Sum(H22) → I22
  118. If(level ≟ true, Sum[list2], Sum[list4]) → a
  119. Sum(H23) → I23