For what value of k will the system be dependent?
x+3y+2z=-4
3x+4y-z=2
3x-y-8z=k
I'm confused as to what exactly it's asking for by a dependent system. I know this is a system with infinite solutions, but I don't know how to find that in 3 dimensions.
If one equation is just a multiple of another one, then the two are equations are dependent
Any row manipulations normally used are allowed
(2)-(3): 5y+7z = 2-k
(3*1)-(2): 5y+7z = -14
So, if 2-k = -14, the system is dependent