Question

Condition for a set of 3 vectors from a basis of real vector space

Answer 1

A vector space's basis is a subset of vectors within the space that are linearly independent, and span the space. A basis is linearly independent because the vectors in it cannot be defined as a linear combination of any of the other vectors in the basis.


These vectors span R3. do not form a basis for R3 because these are the column vectors of a matrix that has two identical rows. The three vectors are not linearly independent. In general, n vectors in Rn form a basis if they are the column vectors of an invertible matrix.

Answer 2

In mathematics, a set B of elements (vectors) in a vector space V is called a basis, if every element of V may be written in a unique way as a (finite) linear combination of elements of B.

The coefficients of this linear combination are referred to as components or coordinates on B of the vector.

The elements of a basis are called basis vectors.