Answer
A set three vectors in $\mathbb{R}^4$ cannot span $\mathbb{R}^4$.
$n$ vectors in $\mathbb{R}^m$ cannot span $\mathbb{R}^m$.
Work Step by Step
For a set of vectors to span $\mathbb{R}^4$, the set of vectors must contain $4$ pivots. However, each vector can contain at most $1$ pivot. Thus, three vectors in $\mathbb{R}^4$, can contain at most $3$ pivots, less than the $4$ pivots needed to span $\mathbb{R}^4$. Thus, a set of three vectors in $\mathbb{R}^4$ cannot span $\mathbb{R}^4$.
Similarly, for $n$ vectors in $\mathbb{R}^m$ to span $\mathbb{R}^m$, the $n$ vectors must contain $m$ pivots. However, because each vector can contain at most 1 pivot, the $n$ vectors can contain at most $n$ pivots. Because the problem states $n$ is less than $m$, the $n$ vectors in $\mathbb{R}^m$ cannot span $\mathbb{R}^m$.
