(a) Give an example of a subspace of V. (b) Write down two different bases of V. (c) Show that the following is a scalar product (-, -) on V : (11. 2) := £a,b, where \b3)
(a) Give an example of a subspace of V. (b) Write down two different bases of V. (c) Show that the following is a scalar product (-, -) on V : (11. 2) := £a,b, where \b3)
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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university level algebra
Transcribed Image Text:1. Let V = R°, the vector space over R of dimension 3.
(a) Give an example of a subspace of V.
(b) Write down two different bases of V.
(c) Show that the following is a scalar product (-, -) on V :
(u. 2) := Ea;b;
y = | b2
b3/
where
u =
a2
i=1
a3
(d) Give an example of a vector in V with length 5.
(e) Use the Gram-Schmidt Process (or otherwise) to find an orthogonal basis for V containing
the vector w =
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