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1. Find the general solution of the differential equation
2. Solve the system
with the initial condition
3. For the matrix
find the eigenvalues and their algebraic and geometric multiplicities. Identify the eigenvectors and,
if applicable, generalized eigenvectors.
4. The system
is solved using the Euler method with step size . Find the resulting approximation
3. The eigenvalues are 2 (algebraically double, geometrically simple) and 3 (simple). The
eigenvector for 3 is (3,2,1), and the eigenvector for 2 is (1,0,0). A generalized
eigenvector is given by (0,1,0).