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Testing for Independent Column Vectors

Testing for Independent Column Vectors
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2017-02-21 03:14
VectorCalculusMatrixGeometric Construction
This example demonstrates how to dynamically test the linear independence of column vectors using GeoGebra. It involves core math concepts like vector spaces, matrix row reduction, linear combinations, and independence determination. Key GeoGebra commands used include Random, Transpose, Element, LaTeX, and ReducedRowEchelonForm to generate random matrices and visualize the computation process. Suitable for high school and above learners for understanding linear algebra fundamentals and matrix applications.

GeoGebra Commands & Parameters

  1. Random(1, 2) → lcpyorn
  2. Random(1, 2) → vorh
  3. Transpose({uh}) → uv
  4. Element({uh, uv}, vorh) → u
  5. Transpose({dwh}) → dwv
  6. Element({{0, 0, 0}, iwh}, lcpyorn) → adjh
  7. Transpose({adjh}) → adjv
  8. Element({adjh, adjv}, vorh) → adj
  9. Transpose({iwh}) → iwv
  10. Transpose({vh}) → vv
  11. Element({vh, vv}, vorh) → v
  12. Random(1, 2) → di
  13. Element({{dwh, dwv}, {iwh, iwv}}, di, vorh) → w
  14. Random(1, 2) → dposorno
  15. Transpose({uh, vh, iwh}) → A
  16. Random(1, 11) → pick
  17. Element({Transpose[{uh, vh}], Transpose[{uh, (c1 * uh)}], Transpose[{uh, vh, iwh}], Transpose[{uh, vh, dwh}], Transpose[{uh, (c1 * uh), vh}], Transpose[{uh, vh, dwh, iwh}], Transpose[{uh, (c1 * uh), vh, (c2 * vh)}], Transpose[{uh, vh, dwh, (c2 * vh), iwh}], Transpose[{uh, (c1 * uh), vh, (c2 * vh)}], Transpose[{uh, (c1 * uh), (c2 * uh), vh, dwh}], Transpose[{uh, vh, iwh, dwh, (c2 * vh)}]}, pick) → B
  18. LaTeX(B) → text1
  19. ReducedRowEchelonForm(B) → Br
  20. LaTeX(Br) → text4