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## Homework Statement

solve the system:

dx/dt = [1 -4] x

_______[4 -7]

with x(0) = [3]

__________[2]

## Homework Equations

## The Attempt at a Solution

I got both eigenvalues of the matrix are -3 and so both eigenvectors are [1]

_____________________________________________________________[1]

so then when I try to solve with the initial condition I get the equation is

Ce^(-3(0))[1] = [3]

__________[1]__[2]

which would lead to C[1] = [3]

__________________[1]___[2]

meaning C = 3 and C = 2 which is impossible because it's the same constant...

Did I get the right eigenvalues and vectors? or is there something I'm missing when it comes to plugging in for the initial condition? Thanks!