anonymous
  • anonymous
Prove that the given subset W is a subspace of V , or show why it is not a subspace of V . V=c∞(R) , W is the set of functions f⊆V for which lim f(x) = 0 x→∞
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
i am going to make a quick guess at no, reasoning that subspace must include the zero vector, V does not
anonymous
  • anonymous
wait, why doesn't V include zero?! the zero function has infinitely many derivitives right?!
anonymous
  • anonymous
oops sorry, i meant W does not include the zero vector

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anonymous
  • anonymous
why doesn't W include the zero function?!
anonymous
  • anonymous
oh lord, i should learn to read. i thought it said \[\lim_{x\to 0}f(x)=\infty\] not the other way around. yes it includes the zero vector! ignore me
anonymous
  • anonymous
ahaha ok, you were scaring me for a sec! i thought i was just starting ot understand this stuff! ok, i'll ask you, for the same question then if it is f(4)=1 instead of the function above, what would the answer be?
anonymous
  • anonymous
answer to first question is yes, since a) zero vector is in W b) a linear combination of elements of Wis also in W c) a scaler multiple of anything in W is in W
anonymous
  • anonymous
for the second question the answer is certainly no
anonymous
  • anonymous
the zero vector is not there
anonymous
  • anonymous
also if f(4)=1 then \[af(4)=a\] not one, so scaler multiples are not there
anonymous
  • anonymous
ok great! thank you!
anonymous
  • anonymous
can i ask you one more by any chance?!
anonymous
  • anonymous
V = M2×2(R), W is the set of matrices whose square is the zero matrix (i.e., those matrices A with A^2 the zero matrix).
TuringTest
  • TuringTest
could you please post this on a new thread?
anonymous
  • anonymous
yep

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