Solve excercise 2.8 Are the following sets of functions linearly independent or dependent?(a) 4e, e, Se(b) cos x, e, 3 sin x(e) 7, x2, 9x, e-Exercise 2.8Are the following sets of functions linearly independent or dependent on the positive -axis?(a) x, x+2, x +5(b) cos x, cos 2x, cos 3x(c) sin x, cos-x, sin 2x(d) x, (x-1)2, (x + 1)(e) sinh x, cosh² x, 1Exercise 2.9Are the following sets of vectors linearly independent or dependent over the complex field?(a) (2,-3, 0), (0, 0, 1), (2i, i, -1)(b) (0, 4, 0), (i, -3i, i), (2, 0, 1)(c) (i, 1, 2), (3, i,-1), (-i,3i, 5i)Exercise 2.10Are the following sets of vectors (in the three-dimensional Euclidean space) linearly indepedent or dependent?(a) (4, 5, 6), (1, 2, 3), (7, 8, 9)(b) (1, 0, 0), (Q, –5, 0), (0,0, /7)(c) (5, 4, 1),(2, 0, -2), (0, 6, –1)2 is also a preExercise 2.11Show that if A is a projection operator, the operator )ator.dess ofExercise 2.12Show that y)(pw1/lw)is a projection ope15 nomal

Answered: Image /qna-images/answer/bf9a3c8d-f2ea-4dd5-b0b5-e88601b14355.jpg

Answered: Exercise 2.8 Are the following sets of…

Exercise 2.8 Are the following sets of functions linearly independent or dependent on the positive x-axis? (a) x, x+2, x +5 (b) cos x, cos 2x, cos 3x (c) sin x, cos x, sin 2x

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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Question

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Solve excercise 2.8

Are the following sets of functions linearly independent or dependent?
(a) 4e, e, Se
(b) cos x, e, 3 sin x
(e) 7, x2, 9x, e-
Exercise 2.8
Are the following sets of functions linearly independent or dependent on the positive -axis?
(a) x, x+2, x +5
(b) cos x, cos 2x, cos 3x
(c) sin x, cos-x, sin 2x
(d) x, (x-1)2, (x + 1)
(e) sinh x, cosh² x, 1
Exercise 2.9
Are the following sets of vectors linearly independent or dependent over the complex field?
(a) (2,-3, 0), (0, 0, 1), (2i, i, -1)
(b) (0, 4, 0), (i, -3i, i), (2, 0, 1)
(c) (i, 1, 2), (3, i,-1), (-i,3i, 5i)
Exercise 2.10
Are the following sets of vectors (in the three-dimensional Euclidean space) linearly indepe
dent or dependent?
(a) (4, 5, 6), (1, 2, 3), (7, 8, 9)
(b) (1, 0, 0), (Q, –5, 0), (0,0, /7)
(c) (5, 4, 1),(2, 0, -2), (0, 6, –1)
2 is also a pre
Exercise 2.11
Show that if A is a projection operator, the operator )
ator.
dess of
Exercise 2.12
Show that y)(pw1/lw)is a projection ope
15 nomal

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