Checking for value that makes vectors linearly dependent
Problem on the past qualifier asks to find the value of h for which the vectors are linearly dependent:
For vectors to be linearly dependent they need to be products of each other multiplied by some coefficient. By mental math I found that with 
vectors are linearly dependent if 
.
Would someone please comment on the correctness and point me to the formulaic way to find such solutions?
Re: Checking for value that makes vectors linearly dependent
I would use:
Where 
Giving the system:
(1) 
(2) 
(3) 
Adding (1) and (2) we find:
Substituting for B into (1) we find:
Substituting for A and B into (3) we find:
=0\:\therefore\:h=-10)
Re: Checking for value that makes vectors linearly dependent
Another way: ![v_1,v_2, v_3\;\textrm{l.d.}\Leftrightarrow \textrm{rank}\;[v_1,v_2,v_3]<3\Leftrightarrow \det\;[v_1,v_2,v_3]=0\Leftrightarrow h=-10](http://latex.codecogs.com/png.latex?v_1,v_2, v_3\;\textrm{l.d.}\Leftrightarrow \textrm{rank}\;[v_1,v_2,v_3]<3\Leftrightarrow \det\;[v_1,v_2,v_3]=0\Leftrightarrow h=-10)
