rather than use the standard definitons of addition and scalar multiplication in R^2, suppose these two operations are defined as follows.(adsbygoogle = window.adsbygoogle || []).push({});

(x1,y1)+(x2,y2)=(x1,0)

c(x,y)=(cx,y)

what would the zero vector be? can it be (0,-y1)? why or why not? I think it should fail this axiom u+0=u.

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# Vector space

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