The statement is true If V is a vector space and S is a subs

The statement is true. If V is a vector space and S is a subset of V, then the span of S is a subspace of V If V is a vector space and S is a subspace of V, then the span of Sis the same as S. If u epsilon 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. The circle of radius 1 centered at the origin in R^2, is a subspace of R^2. Every proper subspace of R^2 can be visualized as being either {(0, 0)} or a line through the origin in R 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 is not a subspace of R^3. If a, b, c, d epsilon R and ad - bc notequalto 0, then the span of {(a) (b), (c)(d)} is all of R^2. There is a vector space V for which the set containing only the zero vector in V is not a subspace of V. R^2 is a subspace of R^3.

Solution

Hello,

Whatever you chose are correct options except for 6th question.

6th is false: Answer is: All proper subspace of R³ is 0 vector or lines passing through origin or planes passing through the origin.

So final answer should be: 1,2,3,5,8.

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Hope it helps!