Two subspaces S and T of $\displaystyle R^4$ are spanned by {(15,1,0,1), (-1,15,0,1) } and { (2,0,1,0), (12, 46, 0, 4), (14, 46, 1, 4)} respectively. Find a basis {X} for $\displaystyle S\cap T$.

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I am suspicious that the question isn't correct, because I found a solution set for $\displaystyle S\cap T$ that is spanned by 2 vectors, not one. Can the dimension of $\displaystyle S\cap T$ really be 1 as the question implies?

BTW, my sol'n set is: (if that's correct)

$\displaystyle S=\lbrace \left( \begin{array}{c}a_1\\a_2\\a_3\\a_4\\a_5 \end{array} \right) =

\left( \begin{array}{c}1\\3\\0\\1\\0 \end{array} \right) a_4 +

\left( \begin{array}{c}1\\3\\-1\\0\\1 \end{array} \right) a_5 \mid a_4,a_5 \in R \rbrace$

(if someone can suggest a better way to typeset column vectors I'd like to know)