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1 1 0 3 9. 1 1 1-2 3 3 2 -1

1 1 0 3 9. 1 1 1-2 3 3 2 -1

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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Number 9 2.4 part a b c and d
a) Find a basis for the nullspace of the matrix. b) Find a basis for the row space of the matrix. c) Find a basis for the column space of the matrix. Do the following for the matrices in Exercises 5–12: b) -2 0. с) 1 15. given (P 1 1 16. Without form: linear combina to the zero pol nomials are lin 17. Show that det(. only if rank(A) 18. Suppose that A m > n, then the d) Determine the rank of the matrix. (Parts (a)-(c) do not have unique answers.) 1 5. 1 19. Suppose that A m < n, then the dent. 1 [ -2 4 6. 20. Consider the li P1(x) = x2 + - nomial p3(x) so basis for P2 in the Lemma 2.11. 21. a) Show that the -1 2 -1 0. 7. -1 1 0 8. 1 -1 -1 1 0 1 1 1 0 3 4 [ 9. 1 1 1 2 -1 -2 10. P2(x) = x² + span P2. 3 3 2 -1 1 0-1 3.
Transcribed Image Text:a) Find a basis for the nullspace of the matrix. b) Find a basis for the row space of the matrix. c) Find a basis for the column space of the matrix. Do the following for the matrices in Exercises 5–12: b) -2 0. с) 1 15. given (P 1 1 16. Without form: linear combina to the zero pol nomials are lin 17. Show that det(. only if rank(A) 18. Suppose that A m > n, then the d) Determine the rank of the matrix. (Parts (a)-(c) do not have unique answers.) 1 5. 1 19. Suppose that A m < n, then the dent. 1 [ -2 4 6. 20. Consider the li P1(x) = x2 + - nomial p3(x) so basis for P2 in the Lemma 2.11. 21. a) Show that the -1 2 -1 0. 7. -1 1 0 8. 1 -1 -1 1 0 1 1 1 0 3 4 [ 9. 1 1 1 2 -1 -2 10. P2(x) = x² + span P2. 3 3 2 -1 1 0-1 3.
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