Are the following statements true or false?1. If the set of vectors U spans a...

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Algebra

Are the following statements true or false?1. If the set of vectors U spans a subspace S, then vectors can be added to U to create a basis for S2. If the set of vectors U spans a subspace S, then vectors can be removed from U to create a basis for 3. If S? and S? are subspaces of R" of the same dimension, then S? = S?.4. If the set of vectors U is linearly independent in a subspace S then vectors can be added to U to create a basis for S5. If the set of vectors U is linearly independent in a subspace S then vectors can be removed from U to create a basis for S.

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Are the following statements true or false?1. If the set of vectors U spans a subspace S, then vectors can be added to U to create a basis for S2. If the set of vectors U spans a subspace S, then vectors can be removed from U to create a basis for 3. If S? and S? are subspaces of R" of the same dimension, then S? = S?.4. If the set of vectors U is linearly independent in a subspace S then vectors can be added to U to create a basis for S5. If the set of vectors U is linearly independent in a subspace S then vectors can be removed from U to create a basis for S.