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A problem on my homework asks us to find a basis for the column space of the following matrix:

\begin{bmatrix}3&-9&6\\-2&6&-4\\1&-3&2\end{bmatrix}

The answer I got is {(3, -2, 1)}

I checked this in two different column space calculators online and one got the same answer as me, but another site had an answer with two vectors in the basis. So I just want to make sure that I got the correct answer? Is the column space one-dimensional or two-dimensional?

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Your answer is correct; so would be any nonzero multiple of it (so it surprises me that the online calculators got "the same answer").

Perhaps your third online attempt involved a typo -- even a single missing minus-sign could change everything -- or it involved a site that didn't do computations correctly. Can you point us to the site that gave the wrong answer?

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    Yes, it's http://www.gregthatcher.com/Mathematics/ColumnSpaceCalculator.aspx I checked for a typo but there wasn't one -- in his version he reduces just to row-echelon form (not all the way to reduced row-echelon form) and used the pivots in that matrix to find the column space – 2017-01-10
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    I just used that site and it produced the correct answer. Sigh. – 2017-01-10