Basis question (Answer check please)

Two subspaces S and T of 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 .

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

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

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