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°.
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°.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Transcribed Image Text: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
α= 90⁰.
81. (1,1, 1, 1), (0, 3, 2, 3),
82. (1,1,1,1), (1,0,3,0),
83. (1,1,0,0), (2,0,1,1),
84. (1,0, 1, 1), (1, 1,2,0),
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. (1,0,1,0), (1,−1,1,−1), (1, 0, 3, —2).
90. (1,1,1,−1), (1,3,0,0), (1,5, 0, 2).
(−3, 5, 1, 1).
(1,0, 5, —2).
(1, −5, 2, 0).
(0, 1, 4, 2).
91. (1,1,1,1), (2,3,0,3), (1,1, −3, 5).
(1, 1, 1, 1), (1,3, 0, 0),
92.
(1,5, 0, -2).
(1,0,0,1), (2, 1, 1,0),
(1,0, 2, –5).
(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),
(1,−1, 3, 3).
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).
93.
94.
(1,0,3,2).
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