LINEAR ALGEBRA
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For more than two vectors: let v1, . . . , vm ? V with m > 2. Must these vectors be linearly independent if no one of them is a scalar multiple of another? If so, prove it. If not, give a counterexample.

NO EVEN IF NONE OF THEM ARE SCALAR MULTIPLES OF OTHER VECTORS ...THEY NEED NOT BE LINEARLY INDEPENDENT ..FOR SIMPLICITY CONSIDER ONLY 3 VECTORS U,V,W ...WITH ..

U=V+W......V=U-W........W=U-V......SO NONE OF THEM ARE SCALAR MULTIPLES OF ANY OTHER VECTOR ..BUT THEY ARE NOT REPEAT NOT LINEARLY INDEPENDENT SINCE WE CAN HAVE ..

C1U+C2V+C3W=0.....WITH...C1=-1,C2=C3=1...THAT IS WITHOUT IMPLYING C1=C2=C3=0...

SO BY DEFINITION OF L.I. , THEY ARE L.D.

IF NONE OF THEM ARE A LINEAR COMBINATION OF ANY OTHER SUB SET OF VECTORS IN THE SET , THEN THEY ARE L.I.