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1 vote
Which of the following are subspaces of R3 ?

(i) (x,y,z)
(ii) (x,y,z)
None of the other choices is correct
(ii) only
(i) and (ii)
(i) only

User Lnu
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1 Answer

6 votes

The correct answer is (i) and (ii). Both of the sets are subspaces of R3 because they satisfy the three criteria of a subspace. The first set, z = (x+y)2, is a set of all triplets (x,y,z) such that z = (x+y)2. The second set, x=10z, is a set of all triplets (x,y,z) such that x = 10z. Neither of the other choices are correct.

User Eric Lecoutre
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