Find bases for the four fundamental subspaces of the matrix A as follows.N(A) = nullspace of AN(AT) = nullspace of ATR(A) = column space of AR(AT) = column space of ATThen show that N(A) = R(AT)+ and N(AT) = R(A)¹.1 1 102 31 3 4N(A) =451↓ 1N(AT)R(A) =↓ 1

We have to find the four fundamental subspaces of the matrix A

Find bases for the four fundamental subspaces of the matrix A as follows. N(AT) = nullspace of AT R(AT) = column space of AT N(A) = nullspace of A R(A) = column space of A Then show that N(A) = R(AT)+ and N(AT) = R(A)+. 1 1 1 023 1 3 4 N(A) = N(AT) = R(A) = ↓ 1 ↓ 1

Find bases for the four fundamental subspaces of the matrix A as follows. N(AT) = nullspace of AT R(AT) = column space of AT N(A) = nullspace of A R(A) = column space of A Then show that N(A) = R(AT)+ and N(AT) = R(A)+. 1 1 1 023 1 3 4 N(A) = N(AT) = R(A) = ↓ 1 ↓ 1

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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Question

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(AT) = R(A)¹.
1 1 1
02 3
1 3 4
N(A) =
451
↓ 1
N(AT)
R(A) =
↓ 1

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