Question

Use eigenvalues and eigenvectors to find the general solution of the following system of differential equations \mathrm{d} / \mathrm{dt} \times(\mathrm{t})=-\mathrm{x}(\mathrm{t}) \quad \mathrm{d} / \mathrm{dt} \mathrm{y}(\mathrm{t})=-4 \mathrm{x}(\mathrm{t})+4 \mathrm{y}(\mathrm{t}) \text { First find the eigenvalues } \lambda_{1}, \lambda_{2} \text { and the corresponding eigenvectors } V_{-} 1, V_{-} 2 \text { of the matrix of coefficients. } \text { Write the eigenvalues in ascending order (that is, } \lambda_{1} \leq \lambda_{2} \text { ): } Write the eigenvectors in their simplest form, without simplifying any fractions that might appear and one of components is 11 or –1–1:

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