SOLUTION: Let v1 and v2 be non zero vectors in a vector space V. Show that the following statements are equivalent. a) v1 is not in Rv2=span{v2} b)Rv1 doesn't equals Rv2

Question 455730: Let v1 and v2 be non zero vectors in a vector space V. Show that the following statements are equivalent.
a) v1 is not in Rv2=span{v2}
b)Rv1 doesn't equals Rv2
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
(a)==>(b): not in ==> for any non-zero real number k.
==> For any non-zero real number m, , and hence no element of span{v1} can be found in span{v2}.
(b) ==> (a): ==> there is element in that is not in , or ,
for any non-zero real number r, or
. Hence v1 is not in span{v2}.
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