Chapter 9 - Systems of Differential Equations - 9.5 Vector Differential Equations: Defective Coefficient Matrix - True-False Review - Page 619: c

False

The number of linearly independent solutions to $x′ = Ax$ corresponding to $\lambda$ is not equal to the dimension of the eigenspace $E_\lambda$. It depends on the multiplicity of the eigenvalues as the roots of the characteristics equation.