Which of the followings are always true? I. A set containing a single vector is linearly independent. II. Every linearly dependent set contains zero vector. III. The set of vectors {kv, v} is linearly dependent for every scalar k. IV. The union of any two subspaces of a vector space V is a subspace V. The set R? is a subspace of R3. O 1, II, V O II, IV, V O 1,II,IV,V O Iv,v O None of them

Question
Which of the followings are always true?
I. A set containing a single vector is linearly independent.
II. Every linearly dependent set contains zero vector.
III. The set of vectors {kv, v} is linearly dependent for every scalar k.
IV. The union of any two subspaces of a vector space V is a subspace
V. The set R? is a subspace of R3.
O 1, II, V
O II, IV, V
O 1,II,IV,V
O Iv,v
O None of them
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Transcribed Image Text

Which of the followings are always true? I. A set containing a single vector is linearly independent. II. Every linearly dependent set contains zero vector. III. The set of vectors {kv, v} is linearly dependent for every scalar k. IV. The union of any two subspaces of a vector space V is a subspace V. The set R? is a subspace of R3. O 1, II, V O II, IV, V O 1,II,IV,V O Iv,v O None of them

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