How can the set {(1,0,0), (0,1,0)} span R^2 when you have 3 coordinates in each vector?

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Shouldn't be the set {(1,0), (0,1)} that spans R^2 ?

I found this here: Linear Span - Examples

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Answer 1 · 2017-06-23T16:30:12

Because the third cohordinate is zero. The set spans #RR^2 times {0}#.

Let the set be S.

#< S > = {v in RR^3 ; v = c (1,0,0) + k (0,1,0) , exists c, k in RR}#

#< S > = {v in RR^3 ; v = (c,0,0) + (0,k,0) , exists c, k in RR}#

#< S > = {v in RR^3 ; v = (c,k,0) , exists c, k in RR}#

#< S > = {(x,y,0) in RR^3 ; forall x, y in RR}#