Above you have the question (b) and it's answer underneath. I am out of the blue as how they proved that it belongs to the nullspace of $A^{T}$?
$\endgroup$61 Answer
$\begingroup$Without knowing exactly what theorems you have access to: The column space of $A$ is orthogonal to left null space of $A$, which is the kernel of $A^T$. The column space is spanned by $q_1$ and $q_2$. Since $q_3$ is orthogonal to both $q_1$ and $q_2$, it is not in the span of $q_1$ and $q_2$, so it is in the left null space.
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