Question

Determine whether or not each of the following
lists of vectors is linearly dependent.
(a) V1 = (1, 2, 5), V2 = (2, 5, 1) and V3 = (1, 5, 2)

Answer 1

0=c1v1+c2v2+c3v3
(0,0,0)=c1(1,2,5)+c2(2,5,1)+c3(1,5,2)
if it has trivial solution then is linear dependent

c1+2c2+c3=0...........................1

Answer 2

if it has only the trivial solution then it is linearly independent*