3. Test the following sets of vectors for linear dependence. Assume the vectors all belong to R, for the appropriate n. a) (1,2,3), (4,5, 6), (7,8, 9) b) (2, 1, 4), (3, 9, 2), (3, 6, 2), (4, 7, 2) c) (1, 1, 1), (1,1,0), (1,0, 0)

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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Please do problem #1, and attached is Exercise 3. Thanks

1. Find bases in echelon form for the vector spaces with the sets of vectors as generators given in parts (a) to (d) of exercise 3.

3. Test the following sets of vectors for linear dependence. Assume the vectors all belong to R, for the
appropriate n.
а) (1, 2, 3), (4,5, 6), (7, 8, 9)
b) (2, 1, 4), (3, 9, 2), (3, 6, 2), (4, 7, 2)
с) (1,1, 1), (1,1, 0), (1, 0, 0)
d) (1,2,5, 7), (3, 2,5, 1), (3, 2, 1, 1), (2, 6, 2, 1)
Transcribed Image Text:3. Test the following sets of vectors for linear dependence. Assume the vectors all belong to R, for the appropriate n. а) (1, 2, 3), (4,5, 6), (7, 8, 9) b) (2, 1, 4), (3, 9, 2), (3, 6, 2), (4, 7, 2) с) (1,1, 1), (1,1, 0), (1, 0, 0) d) (1,2,5, 7), (3, 2,5, 1), (3, 2, 1, 1), (2, 6, 2, 1)
Expert Solution
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To check given vectors are linearly independent or dependent.

Check condition:

  • If Wronskian of vectors is non-zero. Then, vectors are linearly independent in nature.
  • If Wronskian of vectors is zero. Then, vectors are linearly dependent in nature.

Consider a set of vectors V={v1,v2,v3}

Wonskian is calculated as:

W=v1v2v3v1'v2'v3'v1''v2''v3''

 

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