For which h is this set of vectors dependent?

Question

So I have 3 column vectors: $v_1=[1\quad 2\quad 1]$, $v_2=[2\quad 6\quad 3]$ and $v_3=[-1\quad -4\quad h]$. The question now is for what h these vectors are dependent. I got to:

[1 2 -1 0, 0 2 -2 0, 0 0 h+2 0]

But then I get stuck and don't know the answer (and neither the reasoning behind it). h+2=0, but what does -2 do for example? Anyone who can help me? You would be of great help!

Answer 1

HINT

• arrange the vectors as row in a matrix
• perform RREF and set the condition on $h$ to have linear dependence (i.e. #pivots $<3$)