17. For the following questions, find a projection matrix P that projects b onto the column sp- of A, that is, Pb E col(A) and b- Pb is orthogonal to col(A). (i) A = 0 0 0 1 0 0 b = (ii) A = 1 -2 4 830.0 1 -1 1 b

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.6: The Algebra Of Matrices
Problem 13E
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17. For the following questions, find a projection matrix P that projects b onto the column space
of A, that is, Pb E col(A) and b - Pb is orthogonal to col(A).
(i) A =
00]
0 1 0
001
0
0
b =
1
(ii) A =
1
-2 4
-1 1
1
4
7
b =
Transcribed Image Text:17. For the following questions, find a projection matrix P that projects b onto the column space of A, that is, Pb E col(A) and b - Pb is orthogonal to col(A). (i) A = 00] 0 1 0 001 0 0 b = 1 (ii) A = 1 -2 4 -1 1 1 4 7 b =
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