Prove or Disprove -- Linear Algebra

[TheWrathOfMath]

Prove or Disprove: If S= {v1,v2,v3,v4,V5} is a group of five vectors in a linear space V over a field K, so that every linear subset T (S=/=T) is linearly independent over K, then S is also linearly independent over K?

 

[Deleted member 4993]

Prove or Disprove: If S= {v1,v2,v3,v4,V5} is a group of five vectors in a linear space V over a field K, so that every linear subset T (S=/=T) is linearly independent over K, then S is also linearly independent over K?

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[Steven G]

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