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Problem I Let A denote the matrix given below. (i) Find the rank and the nullity of the matrix A. (ii) Find a basis for the row space of A. (iii) Find a basis for the column space of A, then extend it to a basis for R¹.

Problem I Let A denote the matrix given below. (i) Find the rank and the nullity of the matrix A. (ii) Find a basis for the row space of A. (iii) Find a basis for the column space of A, then extend it to a basis for R¹.

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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Problem I Let A denote the matrix given below. (i) Find the rank and the nullity of the matrix A. (ii) Find a basis for the row space of A. (iii) Find a basis for the column space of A, then extend it to a basis for Rª. 4. 7. 10. 13. 16. 19. 1 1 2 2 1 1 2 3 1 1 2 1 -2 0 1 −1 2 1 1 -2 0 20 20-1 1 -2 1 0 2 -1 0 10 -1 1 -2 2 - 1 -2 1 -1 21 −1 1 -2 2 1 -1 22 -1 1 −1 1 2 -1 1 1 1 -2 1 2 1 2-2 1 3 -1 3 2 −1 10 1 -2 20 -1 2 -1 20 1 -2 1 10 -1 2 1 2 -1 -2 1 -1 2 -2 1 1 1 2 1 2 -1 2 2 -2 1 4 1 2 −1 2 2 2 -1 4 1 2. 5. 8. 11. 14. 17. 20. 1 1 -2 -1 1 1 -1 2 1 -1 2 1 -2 -1 2 2 1 1 -1 2 1 1 2 1 1 2 3 1 -2 2 1 -2 2 1 2 1 1 2 -1 2 1 -1 1 -2 -1 −1 2 -1 1 -2 -2 2-2 1 1 1 -1 1 -2 -1 -3 -2 -1 -2 -1 1 -2 -1 2 -1 2 -1 -1 2 -2 -1 -2 -2 1 2 -1 -1 2-2 -1 -2 -2 -2 -2 -4 -1 2-2 1 -1 -1 2 1 2-2 1 4 -1 1 -1 -2 2 2 -2 2 −1 -4 1 3. 6. 9. 12. 15. 18. 1 1 2 1-2 10 -1 2 -1 0 1-2 10 2 -1 1 -1 1 1 −1 1 2 2 -2 2 -20 1-2 1 2 2 -1 2 -2 1 4 2 2 0 -1 1 -2 1 1 -1 2 22 1 -2 -1 3 3 −1 2 -1 -2 0 20 -1 2 1 4 -1 -1 4 -1 -2 -1 -1 -2 2 22 24 22
Transcribed Image Text:Problem I Let A denote the matrix given below. (i) Find the rank and the nullity of the matrix A. (ii) Find a basis for the row space of A. (iii) Find a basis for the column space of A, then extend it to a basis for Rª. 4. 7. 10. 13. 16. 19. 1 1 2 2 1 1 2 3 1 1 2 1 -2 0 1 −1 2 1 1 -2 0 20 20-1 1 -2 1 0 2 -1 0 10 -1 1 -2 2 - 1 -2 1 -1 21 −1 1 -2 2 1 -1 22 -1 1 −1 1 2 -1 1 1 1 -2 1 2 1 2-2 1 3 -1 3 2 −1 10 1 -2 20 -1 2 -1 20 1 -2 1 10 -1 2 1 2 -1 -2 1 -1 2 -2 1 1 1 2 1 2 -1 2 2 -2 1 4 1 2 −1 2 2 2 -1 4 1 2. 5. 8. 11. 14. 17. 20. 1 1 -2 -1 1 1 -1 2 1 -1 2 1 -2 -1 2 2 1 1 -1 2 1 1 2 1 1 2 3 1 -2 2 1 -2 2 1 2 1 1 2 -1 2 1 -1 1 -2 -1 −1 2 -1 1 -2 -2 2-2 1 1 1 -1 1 -2 -1 -3 -2 -1 -2 -1 1 -2 -1 2 -1 2 -1 -1 2 -2 -1 -2 -2 1 2 -1 -1 2-2 -1 -2 -2 -2 -2 -4 -1 2-2 1 -1 -1 2 1 2-2 1 4 -1 1 -1 -2 2 2 -2 2 −1 -4 1 3. 6. 9. 12. 15. 18. 1 1 2 1-2 10 -1 2 -1 0 1-2 10 2 -1 1 -1 1 1 −1 1 2 2 -2 2 -20 1-2 1 2 2 -1 2 -2 1 4 2 2 0 -1 1 -2 1 1 -1 2 22 1 -2 -1 3 3 −1 2 -1 -2 0 20 -1 2 1 4 -1 -1 4 -1 -2 -1 -1 -2 2 22 24 22
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