Problem IV Consider the set of all vectors (x, y, z) € R³ satisfying the following condi-tions. Determine whether it is a subspace of the vector space R³ or not. Briefly explain.61. x-y+z= 0.62. x+y+z= 1.63. x+y=x - 2z = 0.64. x=y=z= 0.65. xyz + 1 = 0.66. x-y=y-z=z-x.67.x=y=0.68. y = z = 1.69. x+y+2z ≥ 0.70. x = y and z ≥ 0.71. xy ≥ 0.72. |x| = y.73. ry20 and |x| = |y|.74. z = x² - y².75. z == x² + y².76. x² + y² + z² = 1.77. x(x - 1) = 0.78. x² + 2y² + 1 = 0.79. xyz = 0.80. xy = y = 0.

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Answered: Problem IV Consider the set of a s.…

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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Problem IV Consider the set of a s. Determine whether it is a subspac 61. z-y +z = 0. 62. x+y+z= 1. 63. x+y=x2z = 0. 64. x=y=z= 0.