subset, then X is linearly dependent. Any subset of V that contains is linearly dependent(since 1.= but 1≠0: 1=0 will mean F ={0}, unacceptable). A set consisting of a non-zero vector is linearly independent. Any subset of a linearly independent set is linearly independent and a superset of linearly dependent set is linearly dependent. Let V be a vector space over a field F. A subset B of V is a basis of V iff (1) V = [B] and (2) B is a linearly independent subset of V. If V is a finite dimensional vector space, it can be proved that any two basis of V contains same number n of elements. N is called dimension of V. Note we can obtain a basis of a subspace generated by given finite number of vectors as seen here:
subset, then X is linearly dependent. Any subset of V that contains is linearly dependent(since 1.= but 1≠0: 1=0 will mean F ={0}, unacceptable). A set consisting of a non-zero vector is linearly independent. Any subset of a linearly independent set is linearly independent and a superset of linearly dependent set is linearly dependent. Let V be a vector space over a field F. A subset B of V is a basis of V iff (1) V = [B] and (2) B is a linearly independent subset of V. If V is a finite dimensional vector space, it can be proved that any two basis of V contains same number n of elements. N is called dimension of V. Note we can obtain a basis of a subspace generated by given finite number of vectors as seen here:
ABSTRACT,LINEAR.docx