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, -1 ≤w, <0 for short positions, and Σω = 0. (c) V is the set of vectors in R2 for which Mv = v, where (2 3¹). M =
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, -1 ≤w, <0 for short positions, and Σω = 0. (c) V is the set of vectors in R2 for which Mv = v, where (2 3¹). M =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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,
-1 < w; < 0 for short positions, and
Σω
W₂ = = 0.
(c) V is the set of vectors in R2 for which Mv = v, where
= (2-3¹).
M =
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