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Suppose A is a real 2x2 matrix with complex eigenvalues α ± i β , β...

Suppose A is a real 2x2 matrix with complex eigenvalues α ± i β , β ≠ 0. It was shown in class that the corresponding eigenvectors will be complex. Suppose that a + i b is an eigenvector for α + i β , for some real vectors a , b . Show that a − i b is an eigenvector corresponding to α − i β . Hint: properties of the complex conjugate may be useful. Please show all work, Thanks

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