Let v1,…,vn∈Rm be a collection of vectors. The Gram matrix of this collection is defined to be the n-by-n matrix whose entry in the ith row and jth column is aij=vi⋅vj, where ⋅ denotes the dot product.
Consider the Gram matrix G of the collection:
v1v2v3v4=(1,2,1)=(−3,5,1)=(0,−3,6)=(4,−2,0).
What is the rank of G?