If A is an (n x n)-matrix of real constants that has a complex eigenvalue and eigenvector v, then the real and imaginary parts of w(t) = elty are linearly independent real-valued solutions of x'=Ax: X₂(t)= Im(w(t)), The matrix in the following system has complex eigenvalues; use the above theorem to find the general (real-valued) solution. 030 -3 0 0 x 005 x(t) = X'= Find the particular solution given the initial conditions. x(t) = x(0) = X₁(t) = Re(w(t)) and

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