General Solution to a Nonhomogeneous System (Variation of Parameters)
This is a video that goes through each step of using variation of parameters to find a particular solution to the nonhomogeneous system, which can then be used with the general solution to the homogeneous system to finally get the general solution to the nonhomogeneous system. Corrections: I believe I said the fundamental matrix is denoted using ξ (Xi/Ksi), but I did mean either Ψ (psi) or Φ (phi) Not sure why I mentioned matrix matrix multiplication at the end. Variation of parameters here only uses matrix vector multiplication for the most part. Undetermined coefficients makes use of matrix matrix multiplication https://drive.google.com/file/d/15D2K... 0:00 Fundamental Matrix 1:39 Ψ inverse 6:15 Ψ inverse times g 8:52 integrating Ψ inverse times g 10:10 Ψ times the integral of Ψ inverse times g dt 15:30 General Solution to the Nonhomogeneous System #linearalgebra #eigenvector #eigenvectors #eigenvalue #eigenvalues #matrix #matrices #differentialequations #systemsofequations #nonhomogeneous #variationofparameters #variation #vector

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