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Additive Property of Determinants

Additive Property of Determinants
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2012-03-09 19:27
VectorMatrixGeometric Construction
In collections Linear Algebra
This example demonstrates the additive property of determinants, showing that the determinant of the sum of two matrices equals the sum of their determinants. It involves core concepts like determinants and matrix addition. Constructed using GeoGebra commands such as Intersect, Vector, Line, and Polygon to visualize matrices and their properties. Suitable for high school and above mathematics learners to understand and verify this important determinant property.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Vector(A, B) → u
  3. Vector(B, C) → v
  4. Vector(A, C) → w
  5. Vector(A, D) → z
  6. Line(B, z) → a
  7. Line(B, z) → b
  8. Line(D, u) → c
  9. Intersect(a, c) → E
  10. Line(E, v) → d
  11. Line(C, a) → e
  12. Intersect(d, e) → F
  13. Polygon(A, B, E, D) → poly1, a_1, b_1, e_1, d_1
  14. Polygon(B, C, F, E) → poly2, b_2, c_1, f, e_2
  15. Polygon(A, C, F, D) → poly3, a_2, c_2, f_1, d_2