Determine whether the following statement is true or false:
Given $A$ $∈$ $M_{m×n}$($\mathbb{R}$) and the zero vector $0$ ∈ $\mathbb{R}^m$, the system of linear equations $A$$\mathbf{x}$ = $0$ always have more than one solution for x
I want to say this is false, but I don't know how to start this proof. Help would be much appreciated.