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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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Subhankar dhara
see it
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Deepak singh 1
any doubt then ask
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Shashi ranjan sinha
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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Shashi ranjan sinha
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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, ka2+ b2,...,kan + bn) also belongs to Rn such that (ka1+b1) +( ka2+b2)+....+ (kan+bn) = k(a1+a2+ ...+an) + (b1+b2+...+bn) = 0. Hence the given set forms a vector space if k=0
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Subhankar dhara
if k=0 then it will be a subspace