Linear Dependency and independency of the vectors
- Krishna Bahadur Bista
Linearly dependent vectors
A finite number of vectors are said to be linearly dependent if any one of them can be expressed as the sum of the remaining vectors. In other words, if there exits an expression of the type such that at least one of the scalars x,y,z,.....t is non-zero then the vectors and are said to be linearly dependent. For example, if then the vectors and are said to be linearly dependent.
Linearly independent vectors
If there exists an expression of the type =0 such that all the scalars x,y,z,......,t are zero then the vectors are said tobe linearly independent. For example, any three non-zero and non-coplanar space vectors connected by the relation are linearly independent from each other because relation be true only when all the scalars x,y,z are zero.