How to determine the span of two vectors in R 2 (4,2) and (1,3)Do I subtract them? I don't how I'd solve this. Thanks in advance. In my question the vectors are like this: [ 4 2 ] But that doesn't matter, right?Would the vector equation x 1 v 1 + x 2 v 2 = b be consistent for any b in R 2 ?

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How to determine the span of two vectors in             R        2  (4,2)  and (1,3)Do I subtract them? I don&#039;t how I&#039;d solve this. Thanks in advance. In my question the vectors are like this:      [                            4                                      2                      ]  But that doesn&#039;t matter, right?Would the vector equation       x    1        v    1    +      x    2        v    2   = b be consistent for any b in             R        2  ?

rmercierm7 · Accepted Answer

The span is just the possible linear combinations of the two vectors...  S  p  a  n  {  (  4  ,  2  )  ,  (  1  ,  3  )  }  =  {  a  (  4  ,  2  )  +  b  (  1  ,  3  )  ;  a  ,  b  ∈      R    }

trkalo84 · Accepted Answer

The span of a set of vectors, is the set of every linear combination that you can &quot;create&quot; from those vectors.So in your example a(4,2)+b(1,3), where   a  ,  b  ∈      R  So for example (5,5) is in the span of your vectors, because   1  ⋅  (  4  ,  2  )  +  1  ⋅  (  1  ,  3  )  =  (  5  ,  5  )Also (3,−1) is in the span as   (  4  ,  2  )  −  (  1  ,  3  )  =  (  3  ,  −  1  )In general every vector of the form   (  4  a  +  b  ,  2  a  +  3  b  ) are in the span.

How to determine the span of two vectors in RR^2: (4,2) and (1,3) Do I subtract them?

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