# The coefficient matrix for a system of linear differential equations of the form y′=Ay has the given eigenvalues and eigenspace bases.

The coefficient matrix for a system of linear differential equations of the form y′=Ay has the given eigenvalues and eigenspace bases. Find the general solution for the system.
$$\lambda_1=2\Rightarrow\left\{\begin{bmatrix}4 \\3 \\1 \end{bmatrix}\right\},\lambda_2=-2\Rightarrow\left\{\begin{bmatrix}1 \\2 \\0 \end{bmatrix},\begin{bmatrix}2 \\3 \\1 \end{bmatrix}\right\}$$

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Derrick
y1=4c1e^2t+c2e^-2t+2c3e^-2t
y2=3c1e^2t+2c2e^-2t+3c^-2t
y3=c1e^2t+x3e^-2t