I have a matrix:

1 a 2a 0 1

0 0 1 -(a+1)/(3a-2) -1/(3a-2)

0 0 0 a^2 - a-2 a^2-3a-4

What values of "a" create infinite solutions with 1 degree of freedom?

What values of "a" create infinite solutions with 2 degree of freedom?

What values of "a" create infinite solutions with 3 degree of freedom?

My problem is...i'm not to sure what degrees of freedom mean? Google and my book both come up pretty short on that definition.

Can somoene please explain in laymans terms what that means?

I know the nullity = 1 or 2 depending if a = -1 or not. "a" can never be -2

I guess the value for a = -2 for 2 degrees of freedom and a != -2 for 1 degree of freedom?