# System of differential equations eigenvalues

• hocuspocus102

## Homework Statement

solve the system:
dx/dt = [1 -4] x
_______[4 -7]
with x(0) = 
__________

## The Attempt at a Solution

I got both eigenvalues of the matrix are -3 and so both eigenvectors are 
_____________________________________________________________
so then when I try to solve with the initial condition I get the equation is
Ce^(-3(0)) = 
____________
which would lead to C = 
_____________________
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!

## Homework Statement

solve the system:
dx/dt = [1 -4] x
_______[4 -7]
with x(0) = 
__________

## The Attempt at a Solution

I got both eigenvalues of the matrix are -3 and so both eigenvectors are 
_____________________________________________________________
so then when I try to solve with the initial condition I get the equation is
Ce^(-3(0)) = 
____________
which would lead to C = 
_____________________
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!
The eigenvalue -3 is repeated, so there is only one eigenvector, <1, 1>, so your work to this point looks fine. Does your text discuss what to do when there are fewer eigenvectors than needed?

no, it only gives examples of how to use 2 different eigenvalues with their corresponding 2 different eigenvectors. is there a different way to do it?

oh ok, thank you very much!