Finding a two-dimensional span given three vectors.

Find the values of k so that the vectors [3 -k -1 0}^T, [-1 2 -k -1]^T, [0 -1 3 -k]^T span a two-dimensional space.

My intuition says that I should form a 4x3 matrix out of these vectors with the first vector as the first column, the second vector as the second column, etc.

Then I should row-reduce until I have only 2 leading ones. This will give me the two vectors that span the two dimensional space, but I am having trouble reducing.

Is this the right approach, or am I doing this incorrectly.

Thanks very much for any help on this topic.