Determine whether the functionsfi(t) = 3t – 5, f2(t) = 3t² + 1, f3(t) = 5t +t|are linearly dependent or linearly independent. If they are linearlydependent, find a linear relation among them.W (f1, f2, f3)If possible, find c1, c2, and c3 such that c1fi + c2f3+ c3f3 = 0NOTE: Enter an expression in terms of f1, f2, and f3, where not all coefficients are 0.If this is not possible, indicate that using the checkbox.= 0not possibleTherefore, f1, f2, and f3 are |Choose onev

Answered: Determine whether the functions fi(t) =…

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

Determine whether the functions
fi(t) = 3t – 5, f2(t) = 3t² + 1, f3(t) = 5t +t
|
are linearly dependent or linearly independent. If they are linearly
dependent, find a linear relation among them.
W (f1, f2, f3)
If possible, find c1, c2, and c3 such that c1fi + c2f3+ c3f3 = 0
NOTE: Enter an expression in terms of f1, f2, and f3, where not all coefficients are 0.
If this is not possible, indicate that using the checkbox.
= 0
not possible
Therefore, f1, f2, and f3 are |Choose onev

Expert Solution

Step 1

In this question, concept of linear dependent is applied.

If there is a nontrivial linear combination of the vectors that equals the zero vector, the collection of vectors is said to be linearly dependent. The vectors are considered to be linearly independent if no such linear combination exists. The definition of dimension is based on these ideas.