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Matrix and Linear Transformation

Matrix and Linear Transformation
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2015-06-22 23:37
VectorCoordinate GeometryMatrixTransformation
This example demonstrates geometrically how a linear transformation is represented using matrices and vectors. Key math concepts include matrices, geometric transformations, and vectors. Constructed with GeoGebra commands like Vector and Sequence, it is suitable for high school students and math enthusiasts learning linear algebra and geometric transformations.

GeoGebra Commands & Parameters

  1. Vector((0, 0), A) → a
  2. Vector((0, 0), B) → u
  3. Vector((0, 0), C) → v
  4. Sequence(Segment[((sgn(x(a)) * i), y(a)), ((sgn(x(a)) * i), 0)], i, 0, abs(x(a))) → list3
  5. Sequence(Segment[(x(a), (sgn(y(a)) * i)), (0, (sgn(y(a)) * i))], i, 0, abs(y(a))) → list4
  6. Sequence(Segment[((sgn(x(a)) * i) * B) + (y(a) * C), ((sgn(x(a)) * i) * B)], i, 0, abs(x(a))) → list2
  7. Sequence(Segment[((sgn(y(a)) * i) * C) + (x(a) * B), ((sgn(y(a)) * i) * C)], i, 0, abs(y(a))) → list1

AI Drawing Prompt Reference

Draw a graph showing how vectors A, B, and C are transformed using matrices. Include the original vectors and the transformed vectors to illustrate the geometric meaning of linear transformations.
The prompt above was compiled from the original drawing commands and is for reference only.