in Vector Analysis retagged by
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If $v_{1},v_{2}, \dots ,v_{6}$ are six vectors in $\mathbb{R}^{4}$ , which one of the following statements is $\text{FALSE}$?

  1. It is not necessary that these vectors span $\mathbb{R}^{4}$.
  2. These vectors are not linearly independent.
  3. Any four of these vectors form a basis for $\mathbb{R}^{4}$.
  4. If $\left \{ v_{1},v_{3},v_{5},v_{6} \right\}$ spans $\mathbb{R}^{4}$ , then it forms a basis for $\mathbb{R}^{4}$.
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