Question 31686
LET US PROVE THIS BY REDUXIO-AD-ABSURDUM OR BY CONTRADICTION.
LET US ASSUME THAT V1 AND V2 ARE NOT LINEARLY INDEPENDENT.
THAT IS THEY ARE LINEARLY DEPENDENT.
SO LET V1=KV2 WHERE K IS A SCALAR.
WE ARE GIVEN 
AV1=V1 ........AKV2=V1....OR......KAV2=V1
BUT AV2=2V2
SO K*2V2=V1
2KV2=V1=2KV2...BUT OUR ASSUMPTION IS V1=KV2
HENCE KV2=2KV2...OR....K=2K...OR....K=0
SO...V1=0V2=0...BUT V1 IS NONZERO VECTOR AS PER HYPOTHESIS.
HENCE THIS IS NOT CORRECT.SO OUR ASSUMPTION THAT V1 AND V2 ARE LINEARLY DEPENDENT IS WRONG.HENCE V1 AND V2 ARE LINEARLY INDEPENDENT.