[Math] Find a matrix whose nullspace is spanned by the vectors $(1,1,1)$ and $(2,1,0)$

Question

I'm no expert at linear agebra, but I have a feeling I made a paper with an impossible question. The question, as stated in the title is:

$V$ is a vector space spanned by the vectors $\displaystyle\begin{pmatrix}1\\1\\1\end{pmatrix}$ and $\displaystyle\begin{pmatrix}2\\1\\0\end{pmatrix}$.

Find a matrix ${\bf B}$ that has $V$ as its null space.

Answer 1

Hint: consider matrices with only one row. If the $\begin{bmatrix} a & b & c \end{bmatrix}$, is a matrix with the desired property, then we must have $a+b+c=0$ and $2a+b=0$. This is an underdetermined system, and so has infinitely many solutions.