anonymous
  • anonymous
show that R x R with the standard addition (x_1,y_1 )+ (x_2,y_2 )=(x_1+x_2,y_1+y_2) and the nonstandard scalar multiplication c(x,y)=(cx,0) is not a vector space.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
this set does not follow the property that 1u=u... suppose if we have any vector v=(v_1,v_2) from R x R then we know that 1v=v if this is really a vector space, however since tthe scalar multiplication here is defined as c(x,y)=(cx,0), then we have, \[1v=1(v_1,v_2)=(1(v_1),0)=(v_1,0)\neq(v_1,v_2)=v\] now we have shown that in this set \[1v \neq v\] and so since this set doesn't have a property of a vector space which is 1v=v, then it is not a vector space

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