Show from first principles, i.e., by using the definition of linear independence,
that if μ = x + iy, y ̸= 0 is an eigenvalue of a real matrix
A with associated eigenvector v = u + iw, then the two real solutions
Y(t) = eat(u cos bt − wsin bt)
Z(t) = eat(u sin bt + wcos bt)
are linearly independent solutions of ˙X = AX.
Use (a) to solve the system (see image)
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