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Chapter 4: Q29E (page 164)

In Problems 27鈥�32, use Definition 1 to determine whether the functions y1and y2are linearly dependent on the interval (0, 1).

29. y1(t) = te2t, y2(t) = e2t

Short Answer

Expert verified

The functions are linearly independent.

Step by step solution

01

Apply the given values.

The functions are y1(t) = te2t, y2(t) = e2t

If the y1 and y2are linearly dependent on the interval (0, 1) then

y1(t) = C1y2(t)

02

Find linearly dependent functions.

Now,

y1(t)=Cy2(t)te2t=Ce2tt=C

Since the function can be written as constant multiple of others, therefore they are linearly independent.

Thus, these functions are linear independent.

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