General Solution to System of Equations w/o Eigenvalues

[hbomb]

I have a question that involves a system of equations that I can't figure out

Give the general solution of the set of equations below:

x'=2x
y'=-x+3y
z'=2x-4y+6z

Hint: While you can use eigenvalues and eigenvectors for this one, there is an easier way to do it.

That's where I'm stuck, I know how to do this using the eigenvalues and eigenvectors.

This is a lower triangular matrix, so the eigenvalues are 2, 3, 6. But what's the other way of doing this?

 

[Office_Shredder]

If x'=2x, what does x equal?

Plug that into the x for y' = -x + 3y, and solve for y.

Do the same for z then.

I find it a bit disconcerting that you have posted so many problems about these types of things, you may want to ask your professor to go over exactly what you're doing, since it looks like you just memorized the matrix formula and left it at that

 

[hbomb]

Yea, he's very vague on some of these topics. He gives examples of finding determinants of matrices and finding eigenvalues and eigenvectors, but he never showed how to solve a system of equations with a given point.