Practice question The next question will not be marked but it is a type of question that is often found in exam papers! a (61). where a is a real parameter.

Use pen and paper to solve 0 2.3-Consider a 2×2 matrix, A= the equation of eigenvalues Det (A-AI) = 0, with I the identity matrix, to find the eigenvalues of matrix A. Find the value a, of the parameter a for which A has repeated real eigenvalues. For values of aa, state the type of eigenvalues of matrix A. Write the Jordan form of matrix A in each different case you found and write the dynamical system it represents in its canonical form. Discuss its critical point(s) and the corresponding stability properties for the different cases you found. Justify your answer.