Proof: Let S ? V be a subset of a vector space V over F. We...

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Basic Math

Proof:
Let S ? V be a subset of a vector space V over F. We have that Sis linearly dependent if and only if there exist vectors v1, v2, .. . , vn ? S such that vi is a linear combination of v1, v2, . . ., vi?1, vi+1, . . . , vn for some 1 ? i ? n.

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Let us first assume that there are vectors v1 v2 vn S such that some vi 1 i n is a linear combination of v1 v2 vi1vi1 vn then there exist scalars a1a2annot all zero if See Answer

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Proof: Let S ? V be a subset of a vector space V over F. We...

90.2K

Verified Solution

Question

Basic Math

Proof:
Let S ? V be a subset of a vector space V over F. We have that Sis linearly dependent if and only if there exist vectors v1, v2, .. . , vn ? S such that vi is a linear combination of v1, v2, . . ., vi?1, vi+1, . . . , vn for some 1 ? i ? n.

Answer & Explanation Solved by verified expert

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Proof: Let S ? V be a subset of a vector space V over F. We...

90.2K

Verified Solution

Question

Basic Math

Proof:Let S ? V be a subset of a vector space V over F. We have that Sis linearly dependent if and only if there exist vectors v1, v2, .. . , vn ? S such that vi is a linear combination of v1, v2, . . ., vi?1, vi+1, . . . , vn for some 1 ? i ? n.

Answer & Explanation Solved by verified expert

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Proof:
Let S ? V be a subset of a vector space V over F. We have that Sis linearly dependent if and only if there exist vectors v1, v2, .. . , vn ? S such that vi is a linear combination of v1, v2, . . ., vi?1, vi+1, . . . , vn for some 1 ? i ? n.