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a subspace of the vector space R³ or not. Briefly explain. 71. ry 2 0. 72. |x| = yl. 73. ry ≥ 0 and |x| = |y|. 74. z = x² - y².

a subspace of the vector space R³ or not. Briefly explain. 71. ry 2 0. 72. |x| = yl. 73. ry ≥ 0 and |x| = |y|. 74. z = x² - y².

Advanced Engineering Mathematics
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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71-74 Please

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.
Transcribed Image Text: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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