Vector Space Span — from Wolfram MathWorld
Excerpt
The span of subspace generated by vectors v_1 and v_2 in V is Span(v_1,v_2)=. A set of vectors m= can be tested to see if they span n-dimensional space using the following Wolfram Language function: SpanningVectorsQ[m_List?MatrixQ] := (NullSpace[m] == )
TOPICS
The span of subspace generated by vectors 
and 
is
A set of vectors 
can be tested to see if they span 
-dimensional space using the following Wolfram Language function:
SpanningVectorsQ[m_List?MatrixQ] :=
(NullSpace[m] == {})
See also
Linear Combination, Null Space, Vector Basis, Vector Space
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Cite this as:
Weisstein, Eric W. “Vector Space Span.” From MathWorld—A Wolfram Web Resource. https://mathworld.wolfram.com/VectorSpaceSpan.html