Problem 6.1. In each of the following, a subset W of some n-space R" is de-fined by means of a given condition imposed on the typical vector (₁,...,In).Determine whether W is a subspace of R".(a) W is the set of all vectors inR³ such that x3 = 0.(b) W is the set of all vectors inR³ such that x₁ = 5x2.(c) W is the set of all vectors inR³ such that x₂ = 1.(d) W is the set of all vectors inR³ such that x₁ + x₂ + x3 = 1.(e) W is the set of all vec-tors in R4 suchx1 + 2x2 + 3x3 + 3x4 0.that(f) W is the set of all vectors inR4 such that ₁ 3x3 andx₂ = 4x4.(g) W is the set of all vectors inR2 such that ₁| = |x₂|.(h) W is the set of all vectors inR2 such that (1₁)² + (x₂)² = 0.(i) W is the set of all vectors inR2 such that (x₁)² + (x₂)² = 1.of all vectors inR2 such that ₁| + |₂| = 1.(j) W is the setof all vectors inR such that x₁ + x₂ = x3 + x4.(k) W is the set(1) W is the set of all vectors inR4 such that ₁2 = x3x4-(m) W is the set of all vectors inR4 such that x1x2x3x4 = 0.(n) W is the set of all vectors inR4 whose components are allnonzero.

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Answered: Problem 6.1. In each of the following,…

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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