Explain the determaine 3.2.1Example AConsider the three functionsf1(k) = 3*, f2(k) = 3k+2, f3(k) = 2*,(3.39)and form the linear combinationcıf1(k)+c2 f2(k) + c3ƒ3 (k) = (c1 + 9c2)3* + c32*.(3.40)For the choice c1 =-9c2, where c2 # 0 and c3given by equation (3.40) is zero. Therefore, we conclude that the functions 3k,0, the linear combination3k+2, and 2* are linearly dependent.Note that the Casoratian for these functions is3k3k+1 3k+3 2k+13k+2 3k+4 2k+23k+2 2kC(k) == 0.(3.41)Again, we reach the conclusion that the above three functions are linearlydependent.

Name: Explain the determaine 3.2.1Example AConsider the three functionsf1(k)
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Description: Explain the determaine 3.2.1Example AConsider the three functionsf1(k) = 3*, f2(k) = 3k+2, f3(k) = 2*,(3.39)and form the linear combinationcıf1(k)+c2 f2(k) + c3ƒ3 (k) = (c1 + 9c2)3* + c32*.(3.40)For the choice c1 =-9c2, where c2 # 0 and c3given by eq

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3.2.1 Example A Consider the three functions f1(k) = 3*, f2(k) = 3k+2, f3(k) = 2*, (3.39) and form the linear combination cifi(k) = +c2 f2(k)+ c3 f3(k) = (cı + 9c2)3k + c32*. (3.40) For the choice c1 = 0, the linear combination -9c2, where c2 7 0 and c3 given by equation (3.40) is zero. Therefore, we conclude that the functions 3*, 3k+2, and 2k are linearly dependent. Note that the Casoratian for these functions is 3k 3k+1 3k+3 2k+1 3k+2 3k+4 2k+2 3k+2 2k C(k) = 0. (3.41) Again, we reach the conclusion that the above three functions are linearly dependent.

3.2.1 Example A Consider the three functions f1(k) = 3, f2(k) = 3k+2, f3(k) = 2, (3.39) and form the linear combination cifi(k) = +c2 f2(k)+ c3 f3(k) = (cı + 9c2)3k + c32. (3.40) For the choice c1 = 0, the linear combination -9c2, where c2 7 0 and c3 given by equation (3.40) is zero. Therefore, we conclude that the functions 3, 3k+2, and 2k are linearly dependent. Note that the Casoratian for these functions is 3k 3k+1 3k+3 2k+1 3k+2 3k+4 2k+2 3k+2 2k C(k) = 0. (3.41) Again, we reach the conclusion that the above three functions are linearly dependent.

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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Explain the determaine

3.2.1
Example A
Consider the three functions
f1(k) = 3*, f2(k) = 3k+2, f3(k) = 2*,
(3.39)
and form the linear combination
cıf1(k)
+c2 f2(k) + c3ƒ3 (k) = (c1 + 9c2)3* + c32*.
(3.40)
For the choice c1 =
-9c2, where c2 # 0 and c3
given by equation (3.40) is zero. Therefore, we conclude that the functions 3k,
0, the linear combination
3k+2, and 2* are linearly dependent.
Note that the Casoratian for these functions is
3k
3k+1 3k+3 2k+1
3k+2 3k+4 2k+2
3k+2 2k
C(k) =
= 0.
(3.41)
Again, we reach the conclusion that the above three functions are linearly
dependent.

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