I have one question about the span thing in linear algebra.

So I got this linear solution, (x1,x2)=t*(-2,1)

But when I have to write the 'span', can I just pick any number for t, such can I write, span for t=-1, so the solution is, span(2,-1)

or the span is just the vector which is being multiplied by t, therefore will it just be, span(-2,1)

Which one is the correct one? Thanks for the help :D

  • $\begingroup$ You can pick any (real) number for t, as long as you avoid choosing zero. $\endgroup$ – A.Sh Dec 7 '15 at 21:25
  • $\begingroup$ @A.Sh doesn't a span include the zero vector? $\endgroup$ – gbox Dec 7 '15 at 21:29
  • $\begingroup$ Yes, the zero vector is included in the span. I thought your question was about what values of t you could use to generate the span. Note that span(0)={0}, since any multiple of the zero vector is zero. However, span(-2,1)=span t(-2,1) for any nonzero (real) value t. $\endgroup$ – A.Sh Dec 7 '15 at 21:32

We say that the span of $(-2,1)$ is the line $\{t(-2,1):t\in\mathbb R\}$; that is, a vector generates its span.


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