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Problem V Let V be a subspace of R4 spanned by three vectors given below. Find the angle a between the vector y (0, 0, 12, 0) and the subspace V. (By definition, a is the angle between y and its orthogonal projection onto V unless y is orthogonal to V, in which case a = 90°. - (−3, 5, 1, 1). (1,0, 5, —2). 81. (1,1, 1, 1), 82. (1,1, 1, 1), (0, 3, 2, 3), (1,0,3,0), 83. (1,1,0,0), (2,0, 1, 1), (1,1,2,0), 84. (1,0, 1, 1), 85. (1,0, 1,0), (1, 1, 1, −1), (1, 2, 3, 0). 86. (1,0,0,1), (0, 1, 1, −2), 87. (1,1,-1, 1), (2,3,0,3), (1,−1, 3, 3). (1, 1, 3, 5). 88. (1,0,0,−1), (2, 1, 1,0), 89. (1,0, 1,0), (1, −1, 1, −1), 90. (1,1,1,−1), (1,3,0,0), (1,5, 0, 2). (1, 0, 2, 5). (1,0, 3, -2). (1, −5, 2, 0). (0, 1, 4, 2). (1,0, 3, 2). 91. (1,1, 1, 1), (2,3,0,3), (1, 1, −3, 5). 92. (1,1, 1, 1), (1,3,0,0), (1,5, 0, -2). 93. (1,0,0,1), (2,1,1,0), (1,0, 2, –5). 94. (1,1,1,0), (1,0, 2, 1), (0, 2, 4, 1). 95. (1,0,1,0), (1,−1, 1, 1), 96. (1,0,1,0), (0, 1, −2, 1), 97. (1,1,1,−1), (2,3,3,0), (1,1,5, 3). 98. (1,0,−1,0), (2,1,0,1), (1,0,5, 2). 99. (1,0,0,1), (1,−1,−1, 1), (1, 0, −2, 3). 100. (1,1,1,1), (1,3,0,0), (1,5,—2, 0). (1, —1, 3, 3).

Problem V Let V be a subspace of R4 spanned by three vectors given below. Find the angle a between the vector y (0, 0, 12, 0) and the subspace V. (By definition, a is the angle between y and its orthogonal projection onto V unless y is orthogonal to V, in which case a = 90°. - (−3, 5, 1, 1). (1,0, 5, —2). 81. (1,1, 1, 1), 82. (1,1, 1, 1), (0, 3, 2, 3), (1,0,3,0), 83. (1,1,0,0), (2,0, 1, 1), (1,1,2,0), 84. (1,0, 1, 1), 85. (1,0, 1,0), (1, 1, 1, −1), (1, 2, 3, 0). 86. (1,0,0,1), (0, 1, 1, −2), 87. (1,1,-1, 1), (2,3,0,3), (1,−1, 3, 3). (1, 1, 3, 5). 88. (1,0,0,−1), (2, 1, 1,0), 89. (1,0, 1,0), (1, −1, 1, −1), 90. (1,1,1,−1), (1,3,0,0), (1,5, 0, 2). (1, 0, 2, 5). (1,0, 3, -2). (1, −5, 2, 0). (0, 1, 4, 2). (1,0, 3, 2). 91. (1,1, 1, 1), (2,3,0,3), (1, 1, −3, 5). 92. (1,1, 1, 1), (1,3,0,0), (1,5, 0, -2). 93. (1,0,0,1), (2,1,1,0), (1,0, 2, –5). 94. (1,1,1,0), (1,0, 2, 1), (0, 2, 4, 1). 95. (1,0,1,0), (1,−1, 1, 1), 96. (1,0,1,0), (0, 1, −2, 1), 97. (1,1,1,−1), (2,3,3,0), (1,1,5, 3). 98. (1,0,−1,0), (2,1,0,1), (1,0,5, 2). 99. (1,0,0,1), (1,−1,−1, 1), (1, 0, −2, 3). 100. (1,1,1,1), (1,3,0,0), (1,5,—2, 0). (1, —1, 3, 3).

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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**Problem V** Let \( V \) be a subspace of \( \mathbb{R}^4 \) spanned by three vectors given below. Find the angle \( \alpha \) between the vector \( \mathbf{y} = (0, 0, 12, 0) \) and the subspace \( V \). (By definition, \( \alpha \) is the angle between \( \mathbf{y} \) and its orthogonal projection onto \( V \) unless \( \mathbf{y} \) is orthogonal to \( V \), in which case \( \alpha = 90^\circ \). 81. \( (1, 1, 1, 1), \, (0, 3, 2, 3), \, (-3, 5, 1, 1) \). 82. \( (1, 1, 1, 1), \, (1, 0, 3, 0), \, (1, 0, 5, -2) \). 83. \( (1, 1, 0, 0), \, (2, 0, 1, 1), \, (1, -5, 2, 0) \). 84. \( (1, 0, 1, 1), \, (1, 1, 2, 0), \, (0, 1, 4, 2) \). 85. \( (1, 0, 1, 0), \, (1, 1, 1, -1), \, (1, 2, 3, 0) \). 86. \( (1, 0, 0, 1), \, (0, 1, 1, -2), \, (1, -1, 3, 3) \). 87. \( (1, 1, -1, 1), \, (2, 3, 0, 3), \, (1, 1, 3, 5) \). 88. \( (1, 0, 0, -1), \, (2, 1, 1, 0), \, (1, 0, 2, 5) \). 89. \( (1,
Transcribed Image Text:**Problem V** Let \( V \) be a subspace of \( \mathbb{R}^4 \) spanned by three vectors given below. Find the angle \( \alpha \) between the vector \( \mathbf{y} = (0, 0, 12, 0) \) and the subspace \( V \). (By definition, \( \alpha \) is the angle between \( \mathbf{y} \) and its orthogonal projection onto \( V \) unless \( \mathbf{y} \) is orthogonal to \( V \), in which case \( \alpha = 90^\circ \). 81. \( (1, 1, 1, 1), \, (0, 3, 2, 3), \, (-3, 5, 1, 1) \). 82. \( (1, 1, 1, 1), \, (1, 0, 3, 0), \, (1, 0, 5, -2) \). 83. \( (1, 1, 0, 0), \, (2, 0, 1, 1), \, (1, -5, 2, 0) \). 84. \( (1, 0, 1, 1), \, (1, 1, 2, 0), \, (0, 1, 4, 2) \). 85. \( (1, 0, 1, 0), \, (1, 1, 1, -1), \, (1, 2, 3, 0) \). 86. \( (1, 0, 0, 1), \, (0, 1, 1, -2), \, (1, -1, 3, 3) \). 87. \( (1, 1, -1, 1), \, (2, 3, 0, 3), \, (1, 1, 3, 5) \). 88. \( (1, 0, 0, -1), \, (2, 1, 1, 0), \, (1, 0, 2, 5) \). 89. \( (1,
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