Linearly Dependent Vectors
Posted on 2007-11-30
n Vectors v_1, v_2, .., v_n, are linearly dependent iff there exist scalars c_1, c_2, .., c_n (not all zero), such that
c_1*v_1 + c_2*v_2 + ... + c_n*v_n = 0.
By this definition, it would seem that the following vectors are linearly dependent:
v_1=(0,0,0), v_2, v_3, .., v_n
(For any c_1 and c_i=0 (for 1<i<=n))
However, this seems (to me) to be on the same par as saying "0 is a multiple of 5"...
So, is there some technicality which resolves this? Are the above linearly dependent or not?