Let V be a vector space and let S = {v,…, Vn} be a set of vectors in V. Prove if the elements of S are linearly dependent, then there exists a vector in S which is a linear combination of the other elements in S.

Q: A set of vectors in V is linearly independent if and only if they form a basis for V. True False

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Q: Let A = U = 1 1 -2 5 0 1 -1 3 24 -6 16 Find a pair of vectors u, v in R4 whose span is the kernel of…

A: The required vectors are  u=⎣⎢⎢⎢⎡​1110​⎦⎥⎥⎥⎤​  ,  v=⎣⎢⎢⎢⎡​−2−301​⎦⎥⎥⎥⎤​  Explanation:

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A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

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Q: 5. Let V be a vector space over R, and suppose that v1, v2, v3, V4 are linearly independent vectors…

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Q: If a set of m vectors in R” is linearly independent, then m ≤ n.

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Q: Let V be a vector space, and assume that the set of vectors {α, β, γ} is a linearly independent set…

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