Use variation of parameters to solve the given nonhomogeneous system. $$\mathbf{X}^{\prime}=\left(\begin{array}{rr} 0 & 2 \\ -1 & 3 \end{array}\right) \mathbf{X}+\left(\begin{array}{c} 2 \\ e^{-3 t} \end{array}\right)$$
Added by Daniel T.
Step 1
To do this, we need to find the eigenvalues and eigenvectors of the matrix A: $$A = \begin{pmatrix} 0 & 2 \\ -1 & 3 \end{pmatrix}$$ The characteristic equation is: $$\det(A - \lambda I) = \begin{vmatrix} -\lambda & 2 \\ -1 & 3-\lambda \end{vmatrix} = \lambda^2 - Show moreโฆ
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