Help with space of vectors that are linear dependent

[nath121]

hi i have a question that i have to show if its true or false

i am given S=(v1,v2,v3) From vector space V

and this question is
1) if S is Linear independent then v3 belongs to span{v1,v2}

 

[wuti]

hi, i think the statement 1) is false. Because thinking v1,v2,v3 as x, y, z axis in R^3. then there is no way you can express x axis with y and z axis alone. So v3 can't belong to span{v1,v2}, as v1 and v2 is a plane and v3 could be a vector not in the plane.

 

[nath121]

hi, i think the statement 1) is false. Because thinking v1,v2,v3 as x, y, z axis in R^3. then there is no way you can express x axis with y and z axis alone. So v3 can't belong to span{v1,v2}, as v1 and v2 is a plane and v3 could be a vector not in the plane.

hi i forgot to add one information that says that S is group of 3 vectors
i said if v3 belongs to span v1 and v2 than v3=av1+bv2 and from here i said (-1)*v3+(a)v1+(b)v2=0 and (-1) is not equal to zero so we got A non-trivial solution and from here i said that S is linear dependent no idea if its right tho thats why im asking if anyone can solve it and show me how he did it

 

[wuti]

I think your proof is correct.