In the "Systems of Differential Equations" section of my Differential Equations and Linear Algebra class, I've gotten to a section called "Vector Formulation". It has seemed simple enough until I got to a question shown below:
Let $\,A\left(t\right)\,$ be an $\,n\times n\,$ matrix function. Prove that the set of all solutions $\,x\,$ to the system: $$x'(t) = A\left(t\right)\,x\left(t\right)$$ is a subspace of $\,V_n\left(I\right)\,$ (the set of all column $\,n$-vector functions on $\,I\,$)
I'm just hoping someone could give me a starting direction here. I know that to prove something is a subspace you have to show closure under addition and scalar multiplication and that it contains the zero vector, but I can't figure out how to begin applying it here. Thanks in advance everyone.