SOLUTION: Prove or show a counterexample. If v1, v2, v3 are vectors in R4 and v3 is not a linear combination of v1 and v2, then {v1, v2, v3} is a linearly independent set.

Algebra ->  College  -> Linear Algebra -> SOLUTION: Prove or show a counterexample. If v1, v2, v3 are vectors in R4 and v3 is not a linear combination of v1 and v2, then {v1, v2, v3} is a linearly independent set.      Log On


   

Question 1135053: Prove or show a counterexample.
If v1, v2, v3 are vectors in R4 and v3 is not a linear combination of v1 and v2, then {v1, v2, v3} is a linearly independent set.
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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The statement is FALSE.

The counterexample is below: 


For example, let  v1  be the zero vector;   let  v2  be the zero vector, too,  and let only v3 is nonzero.


Then  v3  is not a linear combination of v1 and v2,  so the "if" condition is satisfied;  but {v1, v2, v3}  IS NOT linearly independent set.


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