<s>[INST] Showing linear dependence in a matrix Let 
$v_1=\begin{bmatrix}
1\\
-3\\
2\\
\end{bmatrix}
$
Let $V_2=\begin{bmatrix}
-3\\
9\\
-6\\
\end{bmatrix}
$
Let $V_3=\begin{bmatrix}
5\\
-7\\
h\\
\end{bmatrix}
$
For what value of h is the span {v1,v2,v3} linear dependent.
This be my work.
Let $A= \begin{bmatrix}
1 & -3 & 5&  0 \\
-3&9& -7&   0 \\
2& -6 &   h&   0 \\
\end{bmatrix}
$
then doing 3r1+r3 and -2r1+r2
Let $A= \begin{bmatrix}
1 & -3 & 5&  0 \\
0&0& 8&   0 \\
0&0 &   h-10&   0 \\
\end{bmatrix}
$
 [/INST] You must have zeros in last row, so $h+30=0$ and $h=-30$.
</s>