Chapter 9 - Systems of Differential Equations - 9.2 Vector Formulation - True-False Review - Page 592: e

False

For any $n \times n $ linear system, $x'(t)=A(t)x(t)$ always has $n$ linearly independent solutions, regardless of any condition on the determinant. Hence, a $2\times2$ matrix $A$ matrix of constants whose determinant is zero, then the vector differential equation $x′ (t) = Ax(t)$ can have two linearly independent solutions.