Assume $\left\lbrace {\bf u}_1, {\bf u}_2, {\bf u}_3 \right\rbrace$ spans ${\mathbb R}^3$.

Select the best statement.

A. $\lbrace\mathbf{u}_1,\mathbf{u}_2,\mathbf{u}_3,\mathbf{u}_4\rbrace$ spans ${\mathbb R}^3$ unless ${\bf u}_4$ is the zero vector.
B. There is no easy way to determine if $\lbrace\mathbf{u}_1,\mathbf{u}_2,\mathbf{u}_3,\mathbf{u}_4\rbrace$ spans ${\mathbb R}^3$.
C. $\lbrace\mathbf{u}_1,\mathbf{u}_2,\mathbf{u}_3,\mathbf{u}_4\rbrace$ never spans ${\mathbb R}^3$.
D. $\lbrace\mathbf{u}_1,\mathbf{u}_2,\mathbf{u}_3,\mathbf{u}_4\rbrace$ always spans $\mathbb{R}^3$.
E. $\lbrace\mathbf{u}_1,\mathbf{u}_2,\mathbf{u}_3,\mathbf{u}_4\rbrace$ spans ${\mathbb R}^3$ unless ${\bf u}_4$ is a scalar multiple of another vector in the set.
F. none of the above