1. In each case, determine whether V is a vector space. If it is not a...

 

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1. In each case, determine whether V is a vector space. If it is not a vector space, explain why not. If it is, find basis vectors for V. (a) V is the subset of R3 defined by 4x-5y + z = 1. (b) Let the vector w = (w₁, w₂,, wn) represent a portfolio's holdings, where each component w; represents the fraction of the portfolio's total market value in as- set i. Let V be the set of weight vectors that can represent market-neutral long/short portfolios. The weights w, satisfy 0 <w; 1 for long positions, -1w; <0 for short positions, and Σω; = 0. (c) V is the set of vectors in R² for which Mv = v, where M = - (2 3) 1. In each case, determine whether V is a vector space. If it is not a vector space, explain why not. If it is, find basis vectors for V. (a) V is the subset of R3 defined by 4x-5y + z = 1. (b) Let the vector w = (w₁, w₂,, wn) represent a portfolio's holdings, where each component w; represents the fraction of the portfolio's total market value in as- set i. Let V be the set of weight vectors that can represent market-neutral long/short portfolios. The weights w, satisfy 0 <w; 1 for long positions, -1w; <0 for short positions, and Σω; = 0. (c) V is the set of vectors in R² for which Mv = v, where M = - (2 3) 1. In each case, determine whether V is a vector space. If it is not a vector space, explain why not. If it is, find basis vectors for V. (a) V is the subset of R3 defined by 4x-5y + z = 1. (b) Let the vector w = (w₁, w₂,, wn) represent a portfolio's holdings, where each component w; represents the fraction of the portfolio's total market value in as- set i. Let V be the set of weight vectors that can represent market-neutral long/short portfolios. The weights w, satisfy 0 <w; 1 for long positions, -1w; <0 for short positions, and Σω; = 0. (c) V is the set of vectors in R² for which Mv = v, where M = - (2 3) 1. In each case, determine whether V is a vector space. If it is not a vector space, explain why not. If it is, find basis vectors for V. (a) V is the subset of R3 defined by 4x-5y + z = 1. (b) Let the vector w = (w₁, w₂,, wn) represent a portfolio's holdings, where each component w; represents the fraction of the portfolio's total market value in as- set i. Let V be the set of weight vectors that can represent market-neutral long/short portfolios. The weights w, satisfy 0 <w; 1 for long positions, -1w; <0 for short positions, and Σω; = 0. (c) V is the set of vectors in R² for which Mv = v, where M = - (2 3)

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a V is a vector space To determine this we need to check if V satisfies the vector space axioms closure under addition closure under scalar multiplica... View the full answer