🚀 go-pugleaf

On Thu, 3 Jun 1999, Munga Bunga wrote:

> I wanted to know how you can specifically tell if a set of matrix's spans or not. for instance whether (x1,x2,x3) and (y1,y2,y3) span a set and how you can tell.
> or say...
> (x1)        (y1)
> (x2)  and (y2)
> (x3)        (y3)   vectors, and how do you know whether they span or not?

A set of vectors "SS" spans a vector space V when every element in the
space is a linear combination of the vectors in "SS". That is, v element V

	= (sigma for i=1 to n) (c sub i) (v sub i)  
	where v sub i, 1 <= i <= n, are the members of "SS",
	for some coefficients c sub i.

You can tell if a set of vectors is a spanning set because you take some
obvious spanning set of V and make all its members as linear combinations
from the set "SS". It follows that since all v are lc of elements of the
obvious spanning set, they must be lc of elements of "SS" as well.

> 
> im doing  second year uni and the exams comming up, helppppp please.
> if you can email it to me directly i'd appreciate it very much at mb@deskmail.com
> thank you very much.
> 
> 

Warwick Dumas,

keeper of the gerbils


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