SOLUTION: Let v1, v2, v3 be nonzero vectors in R4 where v3 = 3·v2. Show that v1 is a linear combination of v2 and v3 if and only if v1 = a·v2 for some a ∈ R.

Question 1177931: Let v1, v2, v3 be nonzero vectors in R4 where v3 = 3·v2.
Show that v1 is a linear combination of v2 and v3 if and only if v1 = a·v2 for some a ∈ R.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
(==>) Let for some real a.
==> ==> is a linear combination of and .

(<==) Let be a linear combination of and .
==> for some real , .
<==> , by hypothesis.
==> , and therefore for

The statement is thus proved.
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