Given the system Ax b below: -1 2 1 4 1 -1 2 3 (a) Find the Least Squares solution ây of this system. [Hint: if you get awful fractions, check your work!] (b) Find the projection p of b onto the column space of A. [Hint: use x.] (c) Find the residual r = b – p. (d) Verify thatr€ N(A"), i.e., that the residual is in the nullspace of the transpose of A. (e) Did you actually solve the given 4 x 2 system? If not, what 4 x 2 system did you solve? Explain briefly.
Given the system Ax b below: -1 2 1 4 1 -1 2 3 (a) Find the Least Squares solution ây of this system. [Hint: if you get awful fractions, check your work!] (b) Find the projection p of b onto the column space of A. [Hint: use x.] (c) Find the residual r = b – p. (d) Verify thatr€ N(A"), i.e., that the residual is in the nullspace of the transpose of A. (e) Did you actually solve the given 4 x 2 system? If not, what 4 x 2 system did you solve? Explain briefly.
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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![Given the system Ax
b below:
1
2
4
1
X =
1
-1
5
2
3
(a) Find the Least Squares solution x of this system.
[Hint: if you get awful fractions, check your work!]
(b) Find the projection p of b onto the column space of A. [Hint: use x.]
(c) Find the residual r = b – p.
(d) Verify thatre N(A"), i.e., that the residual is in the nullspace of the transpose
of A.
(e) Did you actually solve the given 4 x 2 system? If not, what 4 x 2 system did you
solve? Explain briefly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8d14a18-18b6-4b9f-91b0-8c8acc9b34e2%2Ffcfa0a1e-fe9d-48a9-aba1-221867bb6a82%2Fafoumtv_processed.png&w=3840&q=75)
Transcribed Image Text:Given the system Ax
b below:
1
2
4
1
X =
1
-1
5
2
3
(a) Find the Least Squares solution x of this system.
[Hint: if you get awful fractions, check your work!]
(b) Find the projection p of b onto the column space of A. [Hint: use x.]
(c) Find the residual r = b – p.
(d) Verify thatre N(A"), i.e., that the residual is in the nullspace of the transpose
of A.
(e) Did you actually solve the given 4 x 2 system? If not, what 4 x 2 system did you
solve? Explain briefly.
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