Michael Shelby                                              m-shelby

Assignment 7                                                 Problem 5.1.2

http://people.tamu.edu/~mrs6817/5.1.2.html

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5.1.2

Justify the statement that the span of a set of vectors is the smallest subspace that contains all of those vectors.  (This means that any other subspace that contains all the origional vectors also includes the entire span.)

By definition, a set of vectors can be expressed as a linear combination of the span of the set.  This means that the dimention of the span is the same as the dimention of the set.  Any subspace of the set that has fewer dimentions cannot contain all the vectors in the initial set.  Any subspace that has more dimentions is not a subspace of the set because it is not contained in the initial set.