# Math Help - Textbook Statement Is Confusing

1. ## Textbook Statement Is Confusing

Hi,

This is a page from a text book I am reading:

I can't figure out what the line "(3) and (4) will be basic ..." means. In particular what they mean by "basic".

Any help is very appreciated.

Scott.

2. $\displaystyle e^{\lambda x}\neq 0$. Thus, the characteristic equation holds the only values that will make the equation 0.

$\lambda^2+a\lambda+b \ \mbox{is a quadratic equation which is solved from factoring or the quadratic equation} \ \lambda=\frac{-a\pm\sqrt{a^2-4(1)(b)}}{2(1)}$

3. Thank you, that pushed me in the right direction.

I was thinking basic and basis were related so there was some relation to linear independence. But basic means non-zero variable in the Operations Research sense.