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.

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) (Show Source): You can put this solution on YOUR website!
.
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.

Do not forget to post your "THANKS" to me for my work that I have done for you . . .

RELATED QUESTIONS
Let v1, v2, v3 be nonzero vectors in R4 where v3 = 3·v2. Show that v1 is a linear... (answered by robertb)

Prove that if {v1, v2, v3} is a linearly independent set of vectors, then so are {v1,... (answered by solver91311,rothauserc)

Show that if s=(v1,v2,v3) is a linearly dependent set of vectors in a vector space V, and (answered by robertb)

The voltage V1 and V2 are represented as follows V1 = 3sin(wt) V2 = 2cos(wt) If V3 (answered by ikleyn)

1)In 3d-space, let v1=(0,2,1) v2=(2,1,1) v3=(1,3,-1) v4=(4,2,1). Write v4 as linear... (answered by Fombitz)

This is my second and last question. This is not in a textbook. a.)Let T be a linear... (answered by venugopalramana)

If the set {v1,v2,v3} of vectors of Rm is linearly dependent, then argue that the set... (answered by venugopalramana)

I have a homework problem that I don't know how to do. I'm asked to solve the following (answered by venugopalramana)

If a 4×4 matrix A with rows v1, v2, v3, and v4 has determinant detA=−8, then det [4v1 (answered by ikleyn)