Let $\displaystyle A$ be an m x n matrix. Given $\displaystyle A\bold{x}=\bold{0}$ has nontrivial soln's, in each of the following demonstrate an example if you say yes of $\displaystyle A$ and $\displaystyle \bold{b}$ or if you say no explain why.

Does $\displaystyle \exists\, \bold{b}$ in $\displaystyle \mathbb{R}^m$ such that $\displaystyle A\bold{x}=\bold{b}$ has:

a.) no solution

b.) a unique solution

c.) an infinite # of solutions