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Graphically Finding Eigenvectors of Matrix [[3,1];[0,2]]

Graphically Finding Eigenvectors of Matrix [[3,1];[0,2]]
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2016-12-01 12:32
VectorCoordinate GeometryMatrixGeometric Construction
In collections UNSW MATH1131/1231 Algebra material
This example demonstrates graphically how to find the eigenvectors of the matrix [[3,1];[0,2]]. It involves core mathematical concepts such as eigenvalues, eigenvectors, linear transformations, and matrix operations. The construction uses GeoGebra commands like Intersect, Point, and Vector to geometrically represent eigenvectors. Suitable for high school and above, helping learners understand the geometric significance and practical applications of matrix eigenvectors.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(c) → B
  3. Vector(A, B) → u
  4. Vector(((3 * x(u)) + y(u), (2 * y(u)))) → v

AI Drawing Prompt Reference

On a coordinate plane, mark the origin as a reference point. Draw a vector starting from the origin, with its endpoint lying on a given curve. Then, compute a new vector from the first one using a linear transformation: its x-coordinate equals three times the original x-coordinate plus the original y-coordinate, and its y-coordinate equals twice the original y-coordinate. Draw this new vector also starting from the origin. The final figure shows two vectors from the origin, where the second is the transformed version of the first, illustrating the geometric meaning of eigenvectors.
The prompt above was compiled from the original drawing commands and is for reference only.