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Let $A=\begin{bmatrix} a_{1} & a_{2} & a_{3} \end{bmatrix}$ and $3a_{1}+2a_{2}+a_{3}=0$ where $a_{i}$ are matrix columns. Find the nullspace of $A$.

So, my initial thought was that the nullspace is the span of the vector $\begin{bmatrix} 3\\ 2\\ 1 \end{bmatrix}$, but I'm not quite sure.

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You are right to be not sure, indeed, without any other information what we can say is that the nullspace of $A$ contains the span of $(3,2,1)$ but we can't determine it.

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  • $\begingroup$ +1: For example, $A$ could be the $3\times3$ zero matrix. $\endgroup$ Commented Oct 15, 2018 at 12:21
  • $\begingroup$ @CameronBuie Yes that's really a simple but very effective example! $\endgroup$ Commented Oct 15, 2018 at 12:22

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