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Demonstrating Linear Equations

Demonstrating Linear Equations
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2017-10-05 02:55
VectorCoordinate GeometryParametric EquationGeometric Construction
This example visually demonstrates solving systems of linear equations using vectors and geometric constructs. It involves core math concepts like linear equations, vector operations, and coordinate geometry. GeoGebra commands used include Vector, Invert, Sequence, with objects like Solution, u_i, v_i, T_i. Ideal for high school mathematics education to understand the geometric representation and solution methods of linear equations.

GeoGebra Commands & Parameters

  1. Vector((3.0406485038772604, -1.0975096046860273)) → u_2
  2. Vector((-1.9308039341698673, 3.142269763570411)) → v_{2}
  3. Invert(T_2) → T_{-2}
  4. Vector((0, 1)) → v_{1}
  5. Vector((1, 0)) → u_{1}
  6. Sequence(Line[(T_{1} * (i, 0)), (T_{1} * (i, 1))], i, -10, 10, 1) → L_1
  7. Sequence(Line[(T_{1} * (0, i)), (T_{1} * (1, i))], i, -10, 10, 1) → L_2
  8. Invert(T_{1}) → T_{-1}
  9. Vector((6, 6)) → b
  10. Sequence(Line[(T_s * (i, 0)), (T_s * (i, 1))], i, -10, 10, 1) → L_3
  11. Sequence(Line[(T_s * (0, i)), (T_s * (1, i))], i, -10, 10, 1) → L_4