Eigenvalues, Eigenvectors, and Fibonacci Differential Equation
Loading the math board and drawing, please wait…
This example demonstrates the concepts of eigenvalues and eigenvectors and their application in the Fibonacci differential equation. Key mathematical concepts include eigenvalues, eigenvectors, and differential equations. Using GeoGebra commands such as ApplyMatrix, Sequence, and CurveCartesian, a dynamic demonstration of eigenvectors and eigenvalues is constructed. Suitable for university mathematics students and teachers interested in linear algebra.
GeoGebra Commands & Parameters
ApplyMatrix(M, pic1) → pic1'Sequence(ApplyMatrix[M^(w), pic1], w, 1, k) → l1Sequence((n, (1 / sqrt(5) * (λ_{1}^(n + 1) - λ_{2}^(n + 1)))), n, 0, 8) → l2CurveCartesian(((c_{1} * v_{1}) * ℯ^((λ_{1} * t))) + ((c_{2} * v_{2}) * ℯ^((λ_{2} * t))), t, -5, 5) → sTranslate(v, K) → v_{t}Translate(a_{0}, K) → a_{t}Point(K, v) → GTranslate(s_{t}, G) → u