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

1. In each case, determine whether V is a vector space. If

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 = (w, w,, 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 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 = (w, w,, 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

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