Solving Matrix of Differential Equations With Initial Values

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Homework Statement

Solve the matrix of differential equations with given initial values.

dx/dt= (-6 2) x
(-3 -1)

Initial value is x(0) = -2
-5

Homework Equations

(A-λI)=o

The Attempt at a Solution

My eigenvalues are -4 and 3

My eigenvectors for -4 are 1 and 1 and the eigenvectors for -3 are 1 on the top row and 3/2 on the bottom.

I write out the equations to look like:

C1e^-4t + C2e^-3t
C1e^-4t + 3/2C2e^-3t

I have IVs of -2 on the top row and -5 on the bottom row. To plug these in correctly,do I use the top row values for the top row equation and same for the bottom? If so, I'm getting C1=4 and C2=-6 but this is wrong in our online homework program.

 

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I figured out what I was doing wrong. It was a matter of entering the answer into the online homework program incorrectly, not so much that the answers were wrong.