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Prove the follwing statements Suppose that S is a linearly independent set of vectors in the vector...

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Advance Math

Prove the follwing statements

Suppose that S is a linearly independent set of vectors in thevector space V and let w be a vector of V that isnot in S. Then the set obtained from S by adding wto S is linearly independent in V.

If U is a subspace of a vector space V and dim(U)=dim(V), thenU=V.

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