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4.4.29. For each of the following matrices A, (i) find a basis for each of the four fundamental subspaces; (ii) verify that the image and cokernel are orthogonal complements; (iii) verify that the coimage and kernel are orthogonal complements: 5 (-) ( 2 ). (1) (2) 1 0 (e) 7 3 7 3 12 3 1 4 1 1 2 5 2 203 (f) 2 (c) 1 -2 -3 1 0 1 2 -1 0 -3 (d) -2 3 0 3 1 5 -4 -2 0 -2 2 3 4 4 -1 2 (g) 1 2 0 -1 1 3 0 -1 2 -3 1 1 1 3 3 2 -2 2 2 -5 2 -3 -3 1 4 -5 -2 9 -4 6 -2 -1 2

4.4.29. For each of the following matrices A, (i) find a basis for each of the four fundamental subspaces; (ii) verify that the image and cokernel are orthogonal complements; (iii) verify that the coimage and kernel are orthogonal complements: 5 (-) ( 2 ). (1) (2) 1 0 (e) 7 3 7 3 12 3 1 4 1 1 2 5 2 203 (f) 2 (c) 1 -2 -3 1 0 1 2 -1 0 -3 (d) -2 3 0 3 1 5 -4 -2 0 -2 2 3 4 4 -1 2 (g) 1 2 0 -1 1 3 0 -1 2 -3 1 1 1 3 3 2 -2 2 2 -5 2 -3 -3 1 4 -5 -2 9 -4 6 -2 -1 2

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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7.1.39

4.4.29. For each of the following matrices A, (i) find a basis for each of the four fundamental subspaces; (ii) verify that the image and cokernel are orthogonal complements; (iii) verify that the coimage and kernel are orthogonal complements: 5 (-) ( 2 ). (1) (2) 1 0 (e) 7 3 7 3 12 3 1 4 1 1 2 5 2 203 (f) 2 (c) 1 -2 -3 1 0 1 2 -1 0 -3 (d) -2 3 0 3 1 5 -4 -2 0 -2 2 3 4 4 -1 2 (g) 1 2 0 -1 1 3 0 -1 2 -3 1 1 1 3 3 2 -2 2 2 -5 2 -3 -3 1 4 -5 -2 9 -4 6 -2 -1 2
Transcribed Image Text:4.4.29. For each of the following matrices A, (i) find a basis for each of the four fundamental subspaces; (ii) verify that the image and cokernel are orthogonal complements; (iii) verify that the coimage and kernel are orthogonal complements: 5 (-) ( 2 ). (1) (2) 1 0 (e) 7 3 7 3 12 3 1 4 1 1 2 5 2 203 (f) 2 (c) 1 -2 -3 1 0 1 2 -1 0 -3 (d) -2 3 0 3 1 5 -4 -2 0 -2 2 3 4 4 -1 2 (g) 1 2 0 -1 1 3 0 -1 2 -3 1 1 1 3 3 2 -2 2 2 -5 2 -3 -3 1 4 -5 -2 9 -4 6 -2 -1 2
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