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Vector Space Demonstration

Vector Space Demonstration
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2019-09-17 04:25
VectorCoordinate GeometryMatrix
This example demonstrates the concept of vector space by dynamically adjusting vectors to show the region they span. It involves core mathematical concepts like vector addition, scalar multiplication, linear combinations, and vector space definitions. GeoGebra commands such as Random, If, and ReducedRowEchelonForm are used, along with objects like vectors a1, b1, c1, and matrix M_1, to visualize the space. Suitable for high school students and educators learning linear algebra basics and vector space visualization.

GeoGebra Commands & Parameters

  1. Random(-9, 9) → a1
  2. Random(-2, 2) → scale3
  3. Random(-2, 2) → scale2
  4. Random(-2, 2) → scale1
  5. Random(-9, 9) → b1
  6. Random(0, 1) → test
  7. Random(-9, 9) → a2
  8. Random(-9, 9) → a3
  9. If(test ≟ 0, (scale1 * a1) + (scale2 * b1), (scale1 * a1) + (scale2 * b1) + scale3) → c1
  10. Random(-9, 9) → b2
  11. Random(-9, 9) → b3
  12. If(test ≟ 0, (scale1 * a2) + (scale2 * b2), (scale1 * a2) + (scale2 * b2) + scale3) → c2
  13. If(test ≟ 0, (scale1 * a3) + (scale2 * b3), (scale1 * a3) + (scale2 * b3) + scale3) → c3
  14. ReducedRowEchelonForm({{a1, a2, a3}, {b1, b2, b3}, {c1, c2, c3}}) → M_1