Answer to Question #219748 in Linear Algebra for missaia

Question #219748

Let X = {v1, v2, . . . , vn} be a subset of a vector space V over F. Let

A(X) := {α1v1 + · · · + αnvn | α1 + α2 + · · · + αn = 1}.


Prove that A(X) is a subspace of V if and only if vi = 0V for some i ∈ {1, 2, . . . , n}.


1
Expert's answer
2021-07-27T17:23:38-0400

Answer:-

A(x) is the subspace of V only when:

a) A(x) contains zero vector vector vector (matrix)

b) A(x) is closed under matrix addition an matrix multiplication 

Second condition is already fulfilled so A(x) in the subspace of V only when

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