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Determine whether or not W is a subspace of R3 where W consists of all vectors...

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Question

Basic Math

Determine whether or not W is a subspace of R3 whereW consists of all vectors (a,b,c) in R3 such that

1. a =3b

2. a <= b <= c

3. ab=0

4. a+b+c=0

5. b=a2

6. a=2b=3c

Answer & Explanation Solved by verified expert
4.3 Ratings (878 Votes)
Let X abc and Y def be 2 arbitrary vectors in W and let k be an arbitrary scalar 1 We have a 3b and d 3e so that XY 3bbc3eef 3bebecf This implies that XY W so that W is closed under vector addition Also kX k 3bbc 3kbkbkc This implies that kX W so that W is closed under scalar multiplication Further since 30 0 hence the zero vector000 W Therefore W is a    See Answer
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