# Column vector as a linear combination?

Given this matrix we are asked to answer which column vectors can be written as a linear combination of the others, which is easy, you just create another matrix representing the linear combination and see If it has a solution. I've tried to do so and each one had a solution so I concluded every column vector could; nonetheless, the solution given states that the second column can't be written as a linear combination of the others and I wonder If it's due to some mistake I did that I got a wrong conclusion.

$$\begin{pmatrix} -1 & 1 & 3 & -1\\ 4 & 8 & 0 & 16\\ 2 & 5 & 2 & 9 \end{pmatrix}$$

Let's see... $$2c_1+c_2=c_4$$. The first, second, and fourth columns are linearly dependent, with a relation that can be solved for any one of them in terms of the others. The only one that might not be a linear combination of the others is the third.
If the entries in the three rows are $$a,b,c$$, the first, second, and fourth columns each satisfy $$4a+7b-12c=0$$. The third column doesn't; that column gives $$-12$$ instead.