{( a + b+c+d b – c+ 2d а + 2с — d H = : a, b, c, d e R } C R³, and consider --(}) u = 1 (а) Is u E H? (b) Find a basis of H.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 38EQ
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Questions A and B please 

{(
a + b+c+d
b — с+ 2d
H
: a, b, c, d e R } C R°,
a+ 2с — d
and consider
()
u =
1
(а) Is u € H?
(b) Find a basis of H.
(c) Use Gram-Schmidt to find an orthogonal basis of H
(d) Find the orthogonal projection of u to W.
Transcribed Image Text:{( a + b+c+d b — с+ 2d H : a, b, c, d e R } C R°, a+ 2с — d and consider () u = 1 (а) Is u € H? (b) Find a basis of H. (c) Use Gram-Schmidt to find an orthogonal basis of H (d) Find the orthogonal projection of u to W.
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