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