Chapter 9 - Systems of Differential Equations - 9.8 Matrix Exponential Function and Systems of Differential Equations - True-False Review - Page 642: b

True

Obtain $x'=Ax$ where $X(t)=x_1,x_2,...x_n$ then $e^{At}=X(t)X^{-1}(0)=X_0(t)$ The transition matrix $X_0(t)$ for the vector differential equation $x′ = Ax$ is precisely the same as the matrix exponential function $e^{At}$.