Problem: (a) In (i)-(v), determine whether the given functions are linearly dependent. If they are, give a non-trivial linear combination that is equal to 0. (i) x – 1, x² – 1 and x? – 2x +1 (ii) cos(x), sin(x) and cos(x + ) (iii) x – 1, x² – 2x + 1 and x³ – 3x2 + 3x – 1 -

Problem: (a) In (i)-(v), determine whether the given functions are linearly dependent. If they are, give a non-trivial linear combination that is equal to 0. (i) x – 1, x² – 1 and x? – 2x +1 (ii) cos(x), sin(x) and cos(x + ) (iii) x – 1, x² – 2x + 1 and x³ – 3x2 + 3x – 1 -

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

Problem: (a) In (i)-(v), determine whether the given functions are
linearly dependent. If they are, give a non-trivial linear combination
that is equal to 0.
(i) x – 1, x² –1 and a² – 2x +1
(ii) cos(x), sin(x) and cos(x +
(iii) æ – 1, x² - 2x + 1 and æ³ – 3x² + 3x – 1
(iv) 1, ln(x) and In(2x)
(v) e² and el+z
-

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