The discussion focuses on the linear dynamical system represented by the equation dx/dt = Ax, where A is a matrix. It addresses whether the sum of two solutions, x(t) = x1(t) + x2(t), is also a solution to the system. The consensus is that due to the linearity of the system, the sum of solutions is indeed a solution, which is a fundamental property of linear differential equations.
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Start with this: What does it mean to say that x1(t) and x2(t) are solutions of your matrix differential equation?morsel said: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!