Question

How do you determine the independence(dependence) of a set of vectors by the relation between the number of equations and unknowns in a linear equation? If there are more unknowns than equations then does that mean that they are linearly dependent? Somebody help me plz...

Answer 1

If a vector is written interms of others vectors then we can say tht the vector is depend on that vector..like A=bC..where A and C are vectors and c is constant

Answer 2

*b is constant

Answer 3

for determining linear dependence of vectors say v1 ,v2,v3 .....vn
if we have scalars s1,s2,s3....sn such that
s1v1 +s2v2+s3v3............snvn=0
if and only if each of s1,s2,s3,...sn is 0 thene the vectors are said to be linearly independent
other wise
for at least one of s1,s2,s3,...sn not equal to 0 the relation
s1v1 +s2v2+s3v3............snvn=0 be true then the vectors are linearly dependent..