Suppose $x \in \operatorname{LS}(A,b)$ and $y \in \operatorname{N}(A)$. Show that $x+ty$ is in $\operatorname{LS}(A,b)$ for all $t \in \mathbb{C}$.
Edit: Here $LS(A,b)$ is the set of $x$ such that $Ax=b$, and $N(A)$ is the null space of $A$.
I believe this is considered to be in the category of null space... Because I think that by def. $y-w \in \operatorname{N}(A)$?