Given the system Ax = b below: -1 2 1 4 X= 1-1 3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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I need tha answers for the subquestions a, b, and c. 

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.
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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