Unformatted text preview: 1 e Â¸ 1 t v 21 + c 2 e Â¸ 2 t v 22 Â¾ : In order to determine the eigenvalues of a matrix A , set det( Â¸I Â¡ A ) = 0, where I is the identity matrix, and solve for Â¸ . For each eigenvalue Â¸ , the corresponding eigenvectors are the nonzero solutions v of the matrix equation ( Â¸I Â¡ A ) v = 0. If the 2 Â£ 2 matrix A has repeated eigenvalues Â¸ 1 = Â¸ 2 = Â¸ with only one independent eigenvector v , then one solution is given by x = e Â¸t v . The determination of a second, independent solution is beyond the scope of this course. If the 2 Â£ 2 matrix A has complex eigenvalues, then x 1 = e Â¸ 1 t v 1 and x 2 = e Â¸ 2 t v 2 are two complex solutions. The extraction of two, real, independent solutions from the complex ones is beyond the scope of this course....
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 Winter '09
 Linear Algebra, Systems Of Equations, Equations, Matrices, matrix equation, matrix diÂ®erential equation

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