Solutions to continuous dynamical system

[morsel]

Homework Statement

Consider a linear system dx/dt = Ax of arbitrary size. Suppose x₁(t) and x₂(t) are solutions of the system. Is the sum x(t) = x₁(t) + x₂(t) a solution as well? How do you know?

Homework Equations

The Attempt at a Solution

I have no idea how to go about this problem. Any hints?

Thanks in advance!

 

[Mark44]

Homework Statement

Consider a linear system dx/dt = Ax of arbitrary size. Suppose x₁(t) and x₂(t) are solutions of the system. Is the sum x(t) = x₁(t) + x₂(t) a solution as well? How do you know?

Homework Equations

The Attempt at a Solution

I have no idea how to go about this problem. Any hints?

Thanks in advance!

Start with this: What does it mean to say that x₁(t) and x₂(t) are solutions of your matrix differential equation?