How to show the set {u,v,w} is linearly independent with 2 variables

Question

So the vectors are

r  1   1 
1  s   2 
1  2s  2 

For which values of $r,s$ in subset $\mathbb R$ is the set $\{u,v,w\}$ linearly independent? I got if $s(rs-1)(2r-1)$, does not equal $0$, thus $r$ cannot equal $1/2$, $rs $ cannot equal $1$ and $s$ cannot equal $0$....but i'm feeling $1%$ confident on my answer because the matrices was difficult to reduce to row echelon form Would appreciate any help, Thankyou!

Answer 1

This was asked yesterday by someone else. See the answer here

For which values $r, s \in \mathbb R$ is the set $\{u, v, w\}$ linearly independent?