If $\mathbf{v}_{\mathbf{1}}, \mathbf{v}_{\mathbf{2}} \ldots \mathbf{v}_{\mathbf{6}}$ are six vectors in $\mathbb{R}^4$, which one of the statements is FALSE?
- A
Any four of these vectors form a basis for $\mathbb{R}^4$.
- B
It is not necessary that these vectors span $\mathbb{R}^4$.
- C
If $\left\{\mathbf{v}_1, \mathbf{v}_3, \mathbf{v}_5, \mathbf{v}_6\right\}$ spans $\mathbb{R}^4$, then it forms a basis of $\mathbb{R}^4$.
- D
These vectors are not linearly independent.
✓ Correct answer: A
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