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Let $v_{i}=\left ( v_{i}^{\left ( 1 \right )},v_{i}^{\left ( 2 \right )} ,v_{i}^{\left ( 3 \right )},v_{i}^{\left ( 4 \right )}\right ),$ for $i=1,2,3,4,$ be four vectors in $\mathbb{R}^{4}$ such that $\sum _{i=1}^{4}v_{i}^{\left ( j \right )}=0,$ for each $j=1,2,3,4.$ Let $W$ be the subspace of $\mathbb{R}^{4}$  spanned by $\left \{ v_{1},v_{2},v_{3},v_{4} \right \}$. Then the dimension of $W$ over $\mathbb{R}$ is always

  1. either equal to $1$ or equal to $4$
  2. less than or equal to $3$
  3. greater than or equal to $2$
  4. either equal to $0$ or equal to $4$
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