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..

Quote:

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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..

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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)})

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