Question

In: Advanced Math

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

Prove the follwing statements

Suppose that S is a linearly independent set of vectors in the vector space V and let w be a vector of V that is not in S. Then the set obtained from S by adding w to S is linearly independent in V.

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

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Expert Solution

Q.Prove the following statements

Suppose that S is a linearly independent set of vectors in the vector space V and let w be a vector of V that is not in S. Then the set obtained from S by adding w to S is linearly independent in V.

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

Ans.

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

Colby Messinger answered 9 months ago
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