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# Solving for Eigenvalues

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A certain 4x4 real matrix is known to have these properties:
1) Two of the eigenvalues of A are L1= 3 and L2= 2.
2) The number 3 is an eigenvalue of the matrix A + 2I.
3) det. A = 12.

What are the other 2 eigenvalues of A and what is the characteristic polynomial of A, At, and A-1?

https://brainmass.com/math/linear-algebra/solving-eigenvalues-15516

#### Solution Preview

A certain 4x4 real matrix is known to have these properties:
1) Two of the eigenvalues of A are L1= 3 and L2= 2.
2) The number 3 is an eigenvalue of the matrix A + 2I.
3) det. A = 12.

What are the other 2 eigenvalues of A and what is the characteristic polynomial of A, At, and A-1?

Solution. Assume that is the characteristic polynomial of A. By hypothesis, we know that 3 ...

#### Solution Summary

Eigenvalues are solved. The solution is detailed and well presented.

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