Matrix Transformation of Vectors

Matrix Transformation of Vectors
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2015-12-01 10:01
This GeoGebra example dynamically demonstrates how matrices transform planar vectors, changing their direction and magnitude. Core concepts include matrix multiplication, linear transformations, vector coordinates, and affine mappings. Construction utilizes GeoGebra commands such as Textfield, Element, Intersect, and Polygon, with input boxes allowing dynamic adjustment of matrix elements. The TransformedShape object visualizes the result in real time. Ideal for high school linear algebra, analytic geometry, and university-level introductory mathematics courses seeking visual insights into matrix-vector operations.

GeoGebra Commands & Parameters

  1. Textfield(a) → inputBox1
  2. Textfield(b) → inputBox2
  3. Textfield(c) → inputBox3
  4. Textfield(d) → inputBox4
  5. Element(matrix3, 1, 1) → A_x
  6. Element(matrix3, 2, 1) → A_y
  7. Element(matrix5, 1, 1) → B_x
  8. Element(matrix5, 2, 1) → B_y
  9. Element(matrix7, 1, 1) → C_x
  10. Element(matrix7, 2, 1) → C_y
  11. Intersect(xAxis, yAxis) → D
  12. Element(matrix9, 1, 1) → D_x
  13. Element(matrix9, 2, 1) → D_y
  14. Polygon(C_1, A_1, D_1, B_1) → TrransformedShape, c_1, a_1, d_1, b_1