Question: 3. Let A be a real, square matrix. Suppose it admits a complex eigenvalue = a + ib, where a, be K. (a) By making

3. Let A be a real, square matrix. Suppose it admits a complex eigenvalue = a + ib, where a, be K. (a) By making reference to the characteristic polynomial of A, explain why A = a - ib must also be an eigenvalue. Furthermore, explain why the corresponding eigenvector of A is necessarily complex. (b) Decompose the eigenvector I into real and imaginary parts asc = u tiv. Show that y = u - ju is an eigenvector for A

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