Show that the projection onto Col(A) is unnecessary by verifying that m 타 6 has a unique solution. (This means that 31 1 = 4 4 was already in Col(A).)
Show that the projection onto Col(A) is unnecessary by verifying that m 타 6 has a unique solution. (This means that 31 1 = 4 4 was already in Col(A).)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![If we have a set of points that actually lie on a line, the process we've learned for
linear regression will certainly find the equation of that line! Moreover the linear
model and the input data will match precisely (i.e. all of the residuals will be 0.)
Consider the set of points {(3,4), (4, 5), (6,7)}, and the linear regression proce-
dure.
We would first construct the matrix
31
4 1
6 1
We would normally be solving the system
A
3
4
A.: = V
where vis the projection of the vector made from the y coordinates of the points
onto the column space of A.
Show that the projection onto Col(A) is unnecessary by verifying that
=
1
1
m
b
]
has a unique solution. (This means that
=
4
|;;ª
5
was already in Col(A).)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40e5be32-542f-46cf-9eb7-56d393d1ad35%2F7ddf409d-1f42-4216-a9a9-bfdec9eae607%2F9lqeva_processed.png&w=3840&q=75)
Transcribed Image Text:If we have a set of points that actually lie on a line, the process we've learned for
linear regression will certainly find the equation of that line! Moreover the linear
model and the input data will match precisely (i.e. all of the residuals will be 0.)
Consider the set of points {(3,4), (4, 5), (6,7)}, and the linear regression proce-
dure.
We would first construct the matrix
31
4 1
6 1
We would normally be solving the system
A
3
4
A.: = V
where vis the projection of the vector made from the y coordinates of the points
onto the column space of A.
Show that the projection onto Col(A) is unnecessary by verifying that
=
1
1
m
b
]
has a unique solution. (This means that
=
4
|;;ª
5
was already in Col(A).)
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