let V be a vector space and K a nonempty subset of V prove/disprove :(adsbygoogle = window.adsbygoogle || []).push({});

K is linear independent set iff for every T such that T is a proper subset of K, span(T) is a proper subset of spanK.

im having difficulty finding a counter example, so i think this statement is correct, but how to prove it?

if K is an independent set, then i can show the for every susbset of it its span includes the span of the subset, but if im not mistaken this is correct also when K isnt an independent set.

so my question is how to show that if for every T a proper subset of K, and span{T} a proper subset of span{K}?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A vector space and linear independent set.

Loading...

Similar Threads for vector space linear | Date |
---|---|

I A different way to express the span | Nov 26, 2017 |

B About vector spaces | Jun 12, 2017 |

I Prove the sequence is exact: 0 → ker(f) → V → im(f) → 0 | Dec 4, 2016 |

I Reflexive relation question | Oct 12, 2016 |

I Proof that every basis has the same cardinality | Oct 6, 2016 |

**Physics Forums - The Fusion of Science and Community**