Find bases for the four fundamental subspaces of the matrix A as follows. N(A) = nullspace of A N(AT) =nullspace of AT R(A) = column space of A R(AT) = column space of A Then show that N(A) = R(AT) and N(AT) = R(A)'. 1 1 0 02-3 1-1 3

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 61CR: Find the bases for the four fundamental subspaces of the matrix. A=[010030101].
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Find bases for the four fundamental subspaces of the matrix A as follows.
N(A) nullspace of A N(AT) nullspace of AT
R(A) column space of A R(AT) column space of AT
Then show that N(A) = R(AT) and N(A) = R(A).
1
1
0
0
1-1 3
2-3
3
-3
N(A)-
2
X
↓1
N(AT)-
1
11
1
0
-1
R(A) =
1
3
R(AT) =
x
41
0
2
-3
Transcribed Image Text:Find bases for the four fundamental subspaces of the matrix A as follows. N(A) nullspace of A N(AT) nullspace of AT R(A) column space of A R(AT) column space of AT Then show that N(A) = R(AT) and N(A) = R(A). 1 1 0 0 1-1 3 2-3 3 -3 N(A)- 2 X ↓1 N(AT)- 1 11 1 0 -1 R(A) = 1 3 R(AT) = x 41 0 2 -3
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