5.1.2.html
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.