What does this look like?
I'm given a matrix which has a variable in it, and the question asks to determine the value variable such that the augmented matrix of the linear system has infinitely many solutions.
Determine the value of $\displaystyle h$ such that the matrix is the augmented matrix of a linear system with infinitely many solutions.
$\displaystyle
\begin{array}{c}\ \\ \\ \end{array}\;\begin{vmatrix}\;7 & -7 & 3\;\\\;14 & h & 6\end{vmatrix}
$
That's the exact question.
as Plato hinted, you're on the right track. remember, we have infinitely many solutions if we have some parameter replacing one of our variables. this means there can be no leading 1 in the column that corresponds to that variable. what is the link between that property and one line being a multiple of another?