Determine whether the given functions are linearly dependent or linearly independent. f1(t) = 4t − 5, f2(t) = 4t2 + 1, f3(t) = 5t2 + t linearly dependent linearly independent Correct: Your answer is correct. If they are linearly dependent, find a linear relation among them. (Use f1 for f1(t), f2 for f2(t), and f3 for f3(t). Enter your answer in terms of f1, f2, and f3. If the system is independent, enter INDEPENDENT.)

and linearly dependent.

The required relation is

where a is a nonzero number.

Step-by-step explanation:

Given that,

, and

We consider a linear combination

Putting the value of and

Equating the co-efficient of , t and constant terms

.......(1)

..........(2)

..........(3)

From (2) we get

From (3) we get

Putting the value of in equation (3)

Let [ a is a non zero number]

Then and

We get a nonzero value of , .

Then and linearly dependent.

The required relation is

[a is a nonzero number]

a negative exponent is translated as follows:

so, we have

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step-by-step explanation: