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

Heergerneuu 2022-09-16 Answered
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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Answers (2)

rmercierm7
Answered 2022-09-17 Author has 3 answers
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 }
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trkalo84
Answered 2022-09-18 Author has 2 answers
The span of a set of vectors, is the set of every linear combination that you can "create" 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.
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