MathPlotAI Logo MathPlotAI

Matrix Representation - 3x2

Matrix Representation - 3x2
Loading the math board and drawing, please wait…
2020-04-14 03:01
VectorCoordinate GeometryMatrixGeometric Construction
This example demonstrates how to visualize a 3x2 matrix using vectors in GeoGebra. It involves core mathematical concepts like matrices, vectors, and linear equations. Key GeoGebra commands used include Point, Vector, and Textfield, with objects like A_{11}, A_{21}, A_{12}, A_{22}, A_{13}, and variables L_{X}, L_{Y}, L_{Z}, X, Y, Z, u, v, w, a, b, c, d, e, f, g, h. It is suitable for high school and above students to understand the geometric application of matrices.

GeoGebra Commands & Parameters

  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