iven the system Ax = b below: 2 1 4 1 -1 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 that r E 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.
iven the system Ax = b below: 2 1 4 1 -1 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 that r E 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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I need tha answers for the subquestions d and e.
![Given the system Ax = b below:
-1
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 that r € 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%2F6148ccfe-c9a0-4be7-afce-5e3bffb4b2bf%2Fd5f0e795-5b77-4450-9829-8ae36fcd598a%2F4puqu2a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given the system Ax = b below:
-1
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 that r € 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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