Which of the following statements are true? The statement is true. 1. If V is a

Question

Which of the following statements are true?

The statement is true. 1. If V is a vector space and S is a subset of V, then the span of S is a subspace of V 2. If V is a vector space and S is a subspace of V, then the span of S is the same asS 3. If u E R2 is a nonzero vector, then the span of u is a line through the origin that passes through the point associated with u 4. The circle of radius 1 centered at the origin in R2, is a subspace of R2 5. Every proper subspace of R2 can be visualized as being either ((0,0)or a line through the origin in R2 6. Every proper subspace of R3 can be visualized as being either ((0,0,0)) or a line through the origin in R3 7. R3 is not a subspace of R3 8.Ifa,b,c,d ER and ad-bc # 0, then the span of{C)G)}is all of R2 9. There is a vector space V for which the set containing only the zero vector in V is not a subspace of V o. R2 is a subspace of R3.

Explanation / Answer

1. If V is a vector space and S is a subset of V, then the span of S is a subspace of V
Answer is True
2. If V is a vector space and S is a subspace of V, then the span of S is the same as S
Answer is True
3. If u E R^2 is a nonzero vector, then the span of u is a line through the origin that passes through the point associated with u
Answer is False
4. The circle of radius 1 centered at the origin in R^2, is a subspace of R^2.
Answer is True
5. Every proper subspace of R^2 can be visualized as being either {(0,0)} or a line through the origin in R^2
Answer is True
6. Every proper subspace of R^3 can be visualized as being either ((0,0,0)) or a line through the origin in R^3
Answer is False
7. R3 is not a subspace of R^3
Answer is False
8.Ifa,b,c,d ER and ad-bc # 0, then the span of{C)G)}is all of R^2
Answer is True
9. There is a vector space V for which the set containing only the zero vector in V is not a subspace of V
Answer is False
10. R^2 is a subspace of R^3.
Answer is False

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