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1. If a set S of vectors spans a vector space V, then it is possible to remove one or more vectors from S to create a basis for V. True False 2. If a set S of vectors is linearly independent in a vector space V, then it is possible to add zero or more vectors to S to create a basis for V. True False 3. The set {0} forms a basis for the zero subspace. True False 4. 2. If S = span{ u1, u2, u3 }, then dim(S) = 3 . True False 

          1. If a set S of vectors spans a vector space V, then it is possible to remove one or more vectors from S to create a basis for V.
True
False

2. If a set S of vectors is linearly independent in a vector space V, then it is possible to add zero or more vectors to S to create a basis for V.
True
False

3. The set {0} forms a basis for the zero subspace.
True
False

4. 2. If S = span{ u1, u2, u3 }, then dim(S) = 3 .
True
False
Show more…
1. If a set S of vectors spans a vector space V, then it is possible to remove one or more vectors from S to create a basis for V. True False 2. If a set S of vectors is linearly independent in a vector space V, then it is possible to add zero or more vectors to S to create a basis for V. True False 3. The set 0 forms a basis for the zero subspace. True False 4. 2. If S = span u1, u2, u3 , then dim(S) = 3 . True False

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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1. If a set S of vectors spans a vector space V, then it is possible to remove one or more vectors from S to create a basis for V. True False 2. If a set S of vectors is linearly independent in a vector space V, then it is possible to add zero or more vectors to S to create a basis for V. True False 3. The set {0} forms a basis for the zero subspace. True False 4. If S = span {W1, W2, U1}, then dim(S) = 3. True False
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Transcript

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00:01 Here is the answer for this question is that we have dilution theorem.
00:10 Here let v be a finite dimensional vector space and s be a subset of v such that their pan s is equals to v.
00:46 Then we can remove one or more vectors from s to get a basis of v...
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