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
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-> 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
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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}.
