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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 A Then show that N(A) = R(AT) and N(AT) = R(A)'. 1 1 0 02-3 1-1 3

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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