where * denotes a nonzero number. A = LU= = dim(N(AT)) = 1 and dim(R(AT)) = 4 dim(N(AT)) = 2 and dim(R(AT)) = 2 dim(N(AT)) = 1 and dim(R(A¹)) = 3 dim (N(AT)) = 3 and dim(R(AT)) = 2 dim(N(AT)) = 3 and dim(R(AT)) = 1 dim(N(AT)) = 4 and dim(R(A)) = 1 dim(N(AT)) = 2 and dim(R(A)) = 3 [100 07 1 0 0 ** 10 000 000
where * denotes a nonzero number. A = LU= = dim(N(AT)) = 1 and dim(R(AT)) = 4 dim(N(AT)) = 2 and dim(R(AT)) = 2 dim(N(AT)) = 1 and dim(R(A¹)) = 3 dim (N(AT)) = 3 and dim(R(AT)) = 2 dim(N(AT)) = 3 and dim(R(AT)) = 1 dim(N(AT)) = 4 and dim(R(A)) = 1 dim(N(AT)) = 2 and dim(R(A)) = 3 [100 07 1 0 0 ** 10 000 000
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 30E
Related questions
Question
![Let A be a matrix such that its LU decomposition is of the form
where denotes a nonzero number.
A = LU =
-
dim (N(AT)) = 1 and dim(R(A)) = 4
dim(N(AT)) = 2 and dim(R(A)) = 2
dim(N(A)) = 1 and dim(R(A)) = 3
dim (N(AT)) = 3 and dim(R(A)) = 2
dim(N(AT)) = 3 and dim(R(AT)) = 1
dim(N(AT)) = 4 and dim(R(AT)) = 1
dim(N(AT)) = 2 and dim(R(A)) = 3
[1 0 0 0]
1
0 0
**
10](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8aef4af3-861d-4a67-9526-5e46becfab45%2Fa8099ada-9a96-4119-8997-22128d5d2996%2F9of2ujo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let A be a matrix such that its LU decomposition is of the form
where denotes a nonzero number.
A = LU =
-
dim (N(AT)) = 1 and dim(R(A)) = 4
dim(N(AT)) = 2 and dim(R(A)) = 2
dim(N(A)) = 1 and dim(R(A)) = 3
dim (N(AT)) = 3 and dim(R(A)) = 2
dim(N(AT)) = 3 and dim(R(AT)) = 1
dim(N(AT)) = 4 and dim(R(AT)) = 1
dim(N(AT)) = 2 and dim(R(A)) = 3
[1 0 0 0]
1
0 0
**
10
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