6.Which of the following are subspaces of R ? (x, y, z all belong to R)(i) W{(x, y, z): x + y + z = 0}{(x, y, z): x 2 0}(iii) W = {(x» y, z): x² + y² + ?<1}%3D(ii)W%3D(iv) W{(x, y, z): x, y, z are rationals}{(x> 0, z)}(vi) W = {(x» y» z), y² = x + z}(v) W(vii) W{(x» y, z), 2x + 3y – 4z = 0}

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Answered: 6. Which of the following are subspaces…

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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6. Which of the following are subspaces of R° ? (x, y, z all bclong to R) (i) W {(x, y, z): x + y + z = 0} %3! (ii) W {(x, y, z): x 2 0} %3D (iii) W = {(x» y» z): x² + y³ + z² s 1}