if given that the determinant of a 3 by 3 matrix with only one real entries is 82 and an eigenvalue is given to be 4+5i, what are the other eigenvalues? Since the determinant is a non zero number, I am having a hard time figuring out how to do this.
closed as too broad by GNUSupporter 8964民主女神 地下教會, Don Thousand, max_zorn, user10354138, Leucippus Oct 31 '18 at 4:05
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a 3x3 real matrix has up to 3 eigenvalues, since one of them is known to be complex, its conjugate is also an eigenvalue the third eigenvalue x must be real the determinant equals the product of eigenvalues Therefore (4+5i)*(4-5i)*x = 82 Solve for x, you're done