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Shamsun Asked a Question
August 28, 2020 5:04 pmpts 30 pts
  • IIT JAM
  • Mathematics (MA)

What about (iv)

Hence W is a subspace of V3 (i). vectors (@1, 2, an) in R" are subspaces of R" (n> 3)? Example 7. Which of the following8 sets of all all a such that a 0; (i) all a such that a3 is an integer (iii) all a such that a2+4a3=0; (iv) all a such that ai+a2t... +a,=k (a given constant) Salntion () Let W=la: a E R" and ai 0}.
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  • Piyush Best Answer
    PFA.
    • cropped8046422443501947159.jpg
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    Piyush
    If k =0 then it is a subspace of dim=n-1
  • Anonymous User thankyou
    suppose k =0....... (a1,a2, a3,...., an) and ( b1,b2, b3,...,bn) belongs to the given set and k be the scalar in R. Then, k (a1,a2, a3,...., an) + ( b1,b2, b3,...,bn) = ( ka1+b1, k...
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  • Deepak singh
    see attached , it will clear your doubt..
    • cropped604563594.jpg
    • cropped-1132175713.jpg
    • cropped2037320801.jpg
    Likes(1) Reply(1)
    Shamsun
    great explanation.. thank you sir
  • Anonymous User
    in case k is non zero, then it doesn't form vector space because (0,0,...,0) doesn't belong to the set
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  • Deepak singh
    any doubt then ask
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  • Subhankar dhara
    see it
    • cropped1614452909.jpg
    Likes(1) Reply(0)
  • Subhankar dhara
    if k=0 then it will be a subspace
    Likes(1) Reply(0)
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