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# Find the eigenvalues of A by solving the equation p(x) = 0. (Hint: you should obtain three distinct values.)

INSTRUCTIONS TO CANDIDATES
###### ANSWER ALL QUESTIONS

Consider the following matrix

210 23

1. Compute the characteristic polynomial of A:

p(x) = det(A - I)

2. Find the eigenvalues of A by solving the equation p(x) = 0. (Hint: you should obtain three distinct values.)

3. For each eigenvalue r you obtained, compute a corresponding eigenvector, by solving

the equation Ay

4. Construct a matrix U having as columns the eigenvectors obtained at point 3. Calculate U-1, the inverse of U.

5. Compute U-1AU and verify that the result is a diagonal matrix, having the eigenvalues of A as its diagonal entries.

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