If a 2x2 matrix has trace equal to 9 and determinant equal to 20, what is its larger eigenvalue?

Answer Key:

5

### Solution: Eigenvalues satisfy \lambda^2 - (trace)\lambda + det = 0 ==> \lambda^2 - 9\lambda + 20 = 0 ==> (\lambda - 4)(\lambda - 5) = 0. The eigenvalues are 4 and 5; larger is 5. Correct: 5.

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