Consider the subspaces $$U=\text{span} \lbrace \left[\begin{array}{ccc} 3 &5 &0 \end{array}\right],\left[\begin{array}{ccc} 0 &12 &-6 \end{array}\right] \rbrace$$ and $$W=\text{span} \lbrace \left[\begin{array}{ccc} -3 &2 &-1 \end{array}\right],\left[\begin{array}{ccc} -15 &7 &-11 \end{array}\right] \rbrace$$
of $V={\mathbb R}^{1\times 3}$. Find a matrix $X\in V$ such that $U\cap W = \text{span} \lbrace X \rbrace$.

$X=$$\left[\Rule{0pt}{1.2em}{0pt}\right.$$\left]\Rule{0pt}{1.2em}{0pt}\right.$