Answer
A$\vec x$=$\vec b$ cannot be consistent for all vectors b in $\mathbb{R}^{3}$.
For any mxn matrix A with m>n, A$\vec x$=$\vec b$ cannot be consistent for all vectors $\vec b$ in $\mathbb{R}^{m}$.
Work Step by Step
The matrix A is given to be a 3x2 matrix, so it can have at most 2 pivot positions because it has only two columns. Thus, it cannot have a pivot position in every row. By Theorem 4, A$\vec x$=$\vec b$ cannot be consistent for all vectors b in $\mathbb{R}^{3}$.
In general, for any mxn matrix A with m>n, A$\vec x$=$\vec b$ cannot be consistent for all vectors $\vec b$ in $\mathbb{R}^{m}$.
