From Gilbert Strang's textbook Introduction to Linear Algebra (p.159)
Every matrix with full row rank has these properties
$Ax=b$ has a solution for every right side $b$.
The column space is the whole space $R^m$.
Given that the matrix $A$(of dimensions $m \times n$) is full row-rank, all we know is that it has at least $(n-m)$ non-pivot variables. Therefore, $Ax=b$ has infinite solutions. But does infinite solutions imply $1$ or $2$ above (both are equivalent) ?
How does full row rank imply column space is $R^m$ for a $m \times n$ matrix ?