By theorem 6.19 we know that the solution is
wiht λi the eigenvalues of the matrix A and ui, the eigenvalues.
Thus for this case we then obtain the general solution:
Thus we obtain:
The given matrix is the augmented matrix for a system of linear equations
The coefficient matrix for a system of linear differential equations of the form y′=Ay has the given eigenvalues and eigenspace bases. Find the general solution for the system.
Each of the matrices is the final matrix form for a system of two linear equations in the variables x1 and x2. Write the solution of the system.