You have 5 attempts to solve this problem
Review Lecture 23: Linear Systems
Select all the statements below that are true.
A. If $\mathbf{x}_1$ and $\mathbf{x}_2$ are solutions of a linear system $\mathbf{x}' = A\mathbf{x}$, then so is $2\mathbf{x}_1 - 3\mathbf{x}_2$.
B. Given any two solutions $\mathbf{x}_1(t)$ and $\mathbf{x}_2(t)$ of a linear system $\mathbf{x}' = A\mathbf{x}$, then the general solution is $\mathbf{x} = c_1\mathbf{x}_1 + c_2\mathbf{x}_2$, where $c_1, c_2$ are arbitrary constants.
C. A homogeneous system has the form $\mathbf{x}' = A\mathbf{x} + \mathbf{b}$, where $A$ is a square matrix and $\mathbf{b} \neq \mathbf{0}$.
D. Any second order linear differential equation can be written as a 2x2 first order linear differential system.
E. A linear system $\mathbf{x}' = A\mathbf{x} + \mathbf{b}$ has constant coefficients when both $A$ and $\mathbf{b}$ are constants.
F. Any two solutions $\mathbf{x}_1(t)$ and $\mathbf{x}_2(t)$ of a linear system $\mathbf{x}' = A\mathbf{x}$ are called fundamental solutions.
G. A homogeneous system has the form $\mathbf{x}' = A\mathbf{x}$, where $A$ is a square matrix.
H. Two solutions $\mathbf{x}_1(t)$ and $\mathbf{x}_2(t)$ of a linear system $\mathbf{x}' = A\mathbf{x}$ satisfying $\mathbf{x}_1 \neq c\mathbf{x}_2$ are called fundamental solutions.
I. None of the Above
Note: Select all the correct options.
