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:

Re: Checking for value that makes vectors linearly dependent

Another way: