A set of vectors {x,x2,...,x} in R is linearly {x; | i = 1,..., k} =...

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A set of vectors {x₁,x2,...,x} in R" is linearly {₁x; | i = 1,..., k} = 0 is ; i = 1,..., k. A set of vectors {x₁,x2,... Xx} in R" is affinely independent if the unique solution of {₁x₁|i= 1,..., k} = 0 and Σ{A; | i = 1,..., k} = 0 is A₁ = 0 V i = 1, ..., k.. independent if the unique solution of Prove that the following are equivalent: (a) the set of k vectors {x₁,x2,. x} in R" is affinely independent. (b) the set of k-1 vectors (x2-X1, X3-X₁,..., X-X₁} in R" is linearly independent. {[*][*]-[*]} (c) the set of vectors **** in R+1 is linearly independent. A set of vectors {x₁,x2,...,x} in R" is linearly {₁x; | i = 1,..., k} = 0 is ; i = 1,..., k. A set of vectors {x₁,x2,... Xx} in R" is affinely independent if the unique solution of {₁x₁|i= 1,..., k} = 0 and Σ{A; | i = 1,..., k} = 0 is A₁ = 0 V i = 1, ..., k.. independent if the unique solution of Prove that the following are equivalent: (a) the set of k vectors {x₁,x2,. x} in R" is affinely independent. (b) the set of k-1 vectors (x2-X1, X3-X₁,..., X-X₁} in R" is linearly independent. {[*][*]-[*]} (c) the set of vectors **** in R+1 is linearly independent.

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