span and dimension

• Jul 13th 2013, 07:46 PM
n22
span and dimension
Hello,
I am not sure what to do with the zero vector in this question..thanks.
ﬁnd a basis for Span(X), and say whether or not Span(X) is equal to
the vector space R^n of which X is a subset.

x={(1 2 3),(4 5 6),(0 0 0) which is a subset of R^3

what does one do with the (0 0 0) vector ? is it a multiple of something ?

please note ..each bracketed item represents a column vector not a row vector..
• Jul 13th 2013, 08:10 PM
zzephod
Re: span and dimension
Quote:

Originally Posted by n22
Hello,
I am not sure what to do with the zero vector in this question..thanks.
ﬁnd a basis for Span(X), and say whether or not Span(X) is equal to
the vector space R^n of which X is a subset.

x={(1 2 3),(4 5 6),(0 0 0) which is a subset of R^3

what does one do with the (0 0 0) vector ? is it a multiple of something ?

please note ..each bracketed item represents a column vector not a row vector..

The zero vector does nothing for you as it is already in the space spanned by the other two.

That is: Span(x)=Span({(1 2 3),(4 5 6)})

.