Let S be a subset of Rn What does it mean when we say that S

Let S be a subset of R^n. What does it mean when we say that S spam R^n? Every vector in R^n has exactly one representation as a linear combination of vectors In S. Every vector in R^n can be expressed as a linear combination of vectors In S. The vectors of S are all distinct from each other. S is a basis for R^n. Let S be a subset of R^5 which spans R^5· Then S Must consist of at least five vectors. Must be a basis for R^5. Must be linearly independent. Must have at most five vectors. Must have exactly fine vectors.

Solution

Answer :

4) Let S be a subset of Rⁿ . We define span (S) to be the set of all vectors in Rⁿ that can be written as a linear combination of finitely many elements of S.

Hence , every vector in Rⁿ can be expressed as a linear combination of vectors in S.

5) Let S be a subset of R⁵ which spans R⁵ then S must be a basis of R^5.