- #1

MathematicalPhysicist

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## Main Question or Discussion Point

let V be a vector space and K a nonempty subset of V prove/disprove :

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}?

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}?