Are the following statements true or false? 1. If the set of

Last updated: 7/14/2022

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 S 2. If the set of vectors U spans a subspace S, then vectors can be removed from U to create a basis for 3. If S₁ and S₂ are subspaces of R" of the same dimension, then S₁ = S₂. 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 S 5. 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.