Ok, so I've read this

http://www.mathhelpforum.com/math-he...tml#post356455

But I'm still a bit confused.

My question is this: How do I know when to use $\displaystyle \lambda$ vs $\displaystyle \bar{\lambda}$ to solve.

Here's an example.

$\displaystyle x'_1 = 2x_1-5x_2$

$\displaystyle x'_2=4x_1-2x_2$

So i take

$\displaystyle 0=\begin{vmatrix}2-\lambda &-5\\ 4 &-2-\lambda \end{vmatrix}$

(skip a few steps)

(some quadratic magic)

*poof*

$\displaystyle \lambda = \pm 4i$

Ok, so now, how do I know which is my $\displaystyle \lambda$ which is my $\displaystyle \bar{\lambda}$?

Which one do I use to grind through the rest of this?

Does it matter?

If I solve the matrix for the zero vector using $\displaystyle \lambda = 4i$, I wind up with the vector $\displaystyle \begin{bmatrix}5\\ 2-4i\end{bmatrix}$.

With $\displaystyle \lambda = -4i$, however, I get $\displaystyle \begin{bmatrix}5\\2+4i\end{bmatrix}$.

Given initial conditions, this will effect my result, correct? But it only changes the signs of my constants. Which would be expected since the sign of the equations I end up will will also be opposite?

(sorry if this is a stupid question)