anonymous
  • anonymous
list five elements and determine whether the set is a vector space: (verify the 10 axioms): V={(x,y,z) | z=3}. addition defined by (x1,y1,z1)+(x2,y2,z2) = (x1+x2,y1+y2,3) scalar multiplication defined by s(x,y,z)=(sx,sy,3)
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
list the ten axioms and check. this just fixes z at 3, so it might as well be \[V=\mathbb R^2\]
anonymous
  • anonymous
yea im in the third axiom.. u+(v+w)
anonymous
  • anonymous
for example you can check that \[v_1+v_2=v_2+v_1\]

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anonymous
  • anonymous
and i dont know how to add them
anonymous
  • anonymous
ok \[u+(v+w)=(+)+\]
anonymous
  • anonymous
addition is given by \[(+)=\]
anonymous
  • anonymous
and then \[(+)+\] \[=+\] \[=\]
anonymous
  • anonymous
now do it the other way and see that you get the same thing. that is check that \[+(+)=\] as well
anonymous
  • anonymous
ohh,,, i was adding lol =+ =
anonymous
  • anonymous
stupid me... cool cool i get it

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