Getting quite confused with how to solve this one,

I have 3 vectors v1 (1,1,1) , v2 (1, m , 1) and v3 (1, 1, n)

I'm asked to find m and n that makes v1 - v3 linearly independent - any help would be appreciated

I want to know if I was on the right track - I was thinking that (putting a value which isn't a multiple of 1 i.e. Pi

or make sure that v3 (1, 1, n) the n is not a linear combination of v2's m

ie making v1 (1, 1, 1) , v2 (1, 2, 1) and v3 (1, 1, 5) for example - would that work?

I have the correct answer at the back of the book but would like to know the steps!