Consider the IVP the vector-valued function X Find the eigenvalues lambda_+ and

Question

Consider the IVP the vector-valued function X

Find the eigenvalues lambda_+ and lambda_, larger and smaller or equal or conjugate, respectively, of the coefficient matrix A. Find the eigenvectors v^+ and v^-, satisfying v_1 ^+ = 1 and v_1 ^- =1, respectively. In case the matrix is not diagonalizable, then replace v^- by the vector w defined in the lecture notes, (in the case you need to introduce a vector w, find the one satisfying W_2 = 0), Use the eigenvectors v^+ and, either v^- or w, in (b) to express the corresponding fundamental solutions X^+ and X^-. Find the solution X of the IVP above.

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Consider the IVP the vector-valued function X Find the eigenvalues lambda_+ and

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