-1 1 Let A 24 1 2 10 b= -4 4 The orthogonal projection of b onto Col A and the least-squares solution of Ax=b are [27]

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 62CR
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Question
-1 1
Let A = 24
-12
10
-4
4
The orthogonal projection of b onto Col A and the least-squares solution of Ax=b are
27
4
b. 6= -4
27
4
a.
C.
e.
6.5
6= -4
6.5
1
7
6= -3.5
7
b =
X=
x=
250/33
6--152/33
212/33
17
3
35
6
7
24
x =
-96
11
-38
11
d.
X =
594/101
6= -456/101
716/101
-6
x=
-472
101
122
101
Transcribed Image Text:-1 1 Let A = 24 -12 10 -4 4 The orthogonal projection of b onto Col A and the least-squares solution of Ax=b are 27 4 b. 6= -4 27 4 a. C. e. 6.5 6= -4 6.5 1 7 6= -3.5 7 b = X= x= 250/33 6--152/33 212/33 17 3 35 6 7 24 x = -96 11 -38 11 d. X = 594/101 6= -456/101 716/101 -6 x= -472 101 122 101
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