Find all the values of k for which the following system of polynomialsP1(t) = 2t3 + 4t2 + 4, P2(t) = t,P3(t) = 2t2 + 9t + k, p4(t) = t3 + 8t2 + k? + 7is linearly independent:

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Find all the values of k for which the following system of polynomials P1(t) 2t3 + 4t2 + 4, p2(t) = t, Ps(t) = 2t2 + 9t + k, p4(t) = t + 8t2 + k2 +7 is linearly independent:

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

Find all the values of k for which the following system of polynomials
P1(t) = 2t3 + 4t2 + 4, P2(t) = t,
P3(t) = 2t2 + 9t + k, p4(t) = t3 + 8t2 + k? + 7
is linearly independent:

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