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3×2矩阵表示

3×2矩阵表示
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2020-04-14 03:01
向量解析几何矩阵几何作图
①本范例演示了如何通过GeoGebra绘制3×2矩阵的向量表示；②涉及的核心数学概念包括矩阵、向量、线性方程和几何意义；③作图要点：使用Point、Vector、Textfield命令创建了矩阵元素和向量，涉及A_{11}, A_{21}, A_{12}, A_{22}, A_{13}等对象，并利用L_{X}, L_{Y}, L_{Z}, X, Y, Z, u, v, w, a, b, c, d, e, f, g, h等变量进行交互式展示；④适合高中及以上学生学习和理解矩阵的几何应用。

GeoGebra 命令及参数

  1. Point(L_{X}) → X
  2. Point(L_{Y}) → Y
  3. Point(L_{Z}) → Z
  4. Vector((0, 0), ((A_{11} * x(X)), 0)) → u
  5. Vector(((A_{11} * x(X)), -0.1), ((A_{11} * x(X)) + (A_{12} * x(Y)), -0.1)) → v
  6. Vector(((A_{11} * x(X)) + (A_{12} * x(Y)), -0.2), ((A_{11} * x(X)) + (A_{12} * x(Y)) + (A_{13} * x(Z)), -0.2)) → w
  7. Vector((0, 0), (0, (A_{21} * x(X)))) → a
  8. Vector((-0.1, (A_{21} * x(X))), (-0.1, (A_{21} * x(X)) + (A_{22} * x(Y)))) → b
  9. Vector((-0.2, (A_{21} * x(X)) + (A_{22} * x(Y))), (-0.2, (A_{21} * x(X)) + (A_{22} * x(Y)) + (A_{23} * x(Z)))) → c
  10. Vector(((A_{11} * x(X)) + (A_{12} * x(Y)) + (A_{13} * x(Z)), 0), ((A_{11} * x(X)) + (A_{12} * x(Y)) + (A_{13} * x(Z)), (A_{21} * x(X)) + (A_{22} * x(Y)) + (A_{23} * x(Z)))) → d
  11. Vector((0, (A_{21} * x(X)) + (A_{22} * x(Y)) + (A_{23} * x(Z))), ((A_{11} * x(X)) + (A_{12} * x(Y)) + (A_{13} * x(Z)), (A_{21} * x(X)) + (A_{22} * x(Y)) + (A_{23} * x(Z)))) → e
  12. Vector((0, 0), ((A_{11} * x(X)), (A_{21} * x(X)))) → f
  13. Vector(((A_{11} * x(X)), (A_{21} * x(X))), ((A_{11} * x(X)) + (A_{12} * x(Y)), (A_{21} * x(X)) + (A_{22} * x(Y)))) → g
  14. Vector(((A_{11} * x(X)) + (A_{12} * x(Y)), (A_{21} * x(X)) + (A_{22} * x(Y))), ((A_{11} * x(X)) + (A_{12} * x(Y)) + (A_{13} * x(Z)), (A_{21} * x(X)) + (A_{22} * x(Y)) + (A_{23} * x(Z)))) → h
  15. Textfield(A_{11}) → InputBox1
  16. Textfield(A_{12}) → InputBox2
  17. Textfield(A_{13}) → InputBox3
  18. Textfield(A_{21}) → InputBox4
  19. Textfield(A_{22}) → InputBox5
  20. Textfield(A_{23}) → InputBox6
  21. Vector(((A_{12} * x(Y)), (A_{22} * x(Y)))) → i
  22. Vector(((A_{13} * x(Z)), (A_{23} * x(Z)))) → j