Question

Why word depedent is defination of linearly depedent vectors

Answer 1

Answer:

I'd think about it in terms of a dependence relation you can get. That is, let {v1,v2,…,vn}{v1,v2,…,vn} be linearly dependent. Then there exist scalars a1,a2,…,ana1,a2,…,an, not all zero, so that

a1v1+a2v2+…+anvn=0.

a1v1+a2v2+…+anvn=0.

The above equation is a linear dependence relation, or a linear dependency. There are infinitely many choices for scalars a1,…,ana1,…,an satisfying this equation, but at the same time, not every set of nn numbers will work. You could say that the values for some subset of your aiai's depend on your choices for the others.

Step-by-step explanation: