Take the function on the vector space R3. = 3xıyı+4x2yz+x3y3 Where x = (x1, X2, X3) y = (yı, y2, y3) The given function defines an inner product on R3. 1. Express how , show one basis for it.

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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About basis and inner product:

Take the function on the vector space R3.
<x,y> = 3xıyı+4x2yz+x3y3
Where x = (x1, X2, X3)
y = (yı, y2, y3)
The given function<x,y> defines an inner product on R3.
1. Express how <X defines an inner product on R3.
2. There are bases for the orthogonal complement of {(-2, 3, 1)} with respect to the
inner product <,>, show one basis for it.
Transcribed Image Text:Take the function on the vector space R3. <x,y> = 3xıyı+4x2yz+x3y3 Where x = (x1, X2, X3) y = (yı, y2, y3) The given function<x,y> defines an inner product on R3. 1. Express how <X defines an inner product on R3. 2. There are bases for the orthogonal complement of {(-2, 3, 1)} with respect to the inner product <,>, show one basis for it.
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Can you explain number 2? How did you know that <x,(-2,3,1)> is the formula to use?

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