Let R2 have the weighted Euclidean inner product < u,v>= 3u₁v₁ + 4u₂v2, and let u = [1, 2], v = [-1, 2], w = [3,-1], and k = 2. Compute the stated quantities. a) b) c) d) ||v|| d(u, v)

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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Question
17
a)
b)
e)
Paragraph
O
1. Let R² have the weighted Euclidean inner product <u, v >= 3u₁v₁ +4u₂v₂, and let u
= [1, 2], v = [-1, 2], w = [3,-1], and k = 2. Compute the stated quantities.
a)
b)
<U,V>
<kv, w >
<u+v,w>
||v||
d(u, v)
22
2. In each part, determine whether the set of vectors is orthogonal and whether it is
orthonormal with respect to the Euclidean inner product on R³.
√2
Styles
1
[1,0,0], [0, 1, [0,0,1 ]
₪
Transcribed Image Text:17 a) b) e) Paragraph O 1. Let R² have the weighted Euclidean inner product <u, v >= 3u₁v₁ +4u₂v₂, and let u = [1, 2], v = [-1, 2], w = [3,-1], and k = 2. Compute the stated quantities. a) b) <U,V> <kv, w > <u+v,w> ||v|| d(u, v) 22 2. In each part, determine whether the set of vectors is orthogonal and whether it is orthonormal with respect to the Euclidean inner product on R³. √2 Styles 1 [1,0,0], [0, 1, [0,0,1 ] ₪
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