Question

define the basis of vector space

Answer 1

A set of vectors is said to be a Basis of the -vector space if both and is a linearly independent set. ... We will now look at a very important theorem which defines whether a set of vectors is a basis of a finite-dimensional vector space or not.

Answer 2

Definition: A set of vectors is said to be a Basis of the -vector space if both and is a linearly independent set. ... Theorem 1: A set of vectors from the vector space is a basis if and only if each vector can be written uniquely as a linearly combination of the vectors in , that is .