Computation of eigenvalues

We would like to compute the eigenvalues of the matrix

Recall that an eigenvalue is a number which, together with its eigenvector , solves the equation . We can find by solving the equation . Substituting the matrix A defined above, we get

The characteristic polynomial is equivalent to the determinant of the matrix .

We can compute by using cofactors:

The roots of this cubic polynomial are the three eigenvalues of A:

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