Simple question from a calc 3 beginner. Visually I cannot imagine the span of two vectors, what does this necessarily mean? For example my text mentions if two vectors are parallel their span is a line, otherwise a plane. Can anyone elaborate?
[Math] Geometrically, what is the span of vectors
linear algebravector-spacesvectors
Best Answer
In $R^n$:
If two vectors are linearly dependent their span is the line determined by the vectors (the line made by a vector starting at the origin).
If two vectors are linearly independent their span is the plane.
For three linearly independent vectors the span is the entire three dimensional space.
If the three vectors are linearly dependent then it is either a plane or a line depending on "how linearly dependent" the vectors are.