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The matrix [2, -4; 4, -2] has

1. real eigenvalues and eigenvectors
2. real eigenvalues but complex eigenvectors
3. complex eigenvalues but real eigenvectors
4. complex eigenvalues and eigenvectors

Correct answer: complex eigenvalues and eigenvectors

Solution

The matrix has a negative determinant and a non-zero trace, which indicates that its eigenvalues are complex. Consequently, the eigenvectors associated with these complex eigenvalues are also complex.

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