Matrix-vector differential equation proof

[tracedinair]

Homework Statement

Prove that x(t) = c₁y₁e^-2t + c₂y₁e^5t

is a solution to x' = Ax

given that y₁ is the matrix

( 1 )
( -3 ) and y₂ is the matrix

(2)
(1)

Homework Equations

The Attempt at a Solution

I've never had to do a lot of proofs and I am not really sure of where to start this problem. I know I'm supposed to differentiate X but I don't know how to do so..

 

[lanedance]

hi tracedinair

do you have the matrix A? if so it could be as easy as calculating x' and A.x and showing they are equivalent