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Chapter 4: Q32E (page 164)

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

32. y1(t)= 0, y2(t) = et

Short Answer

Expert verified

The functions are linearly dependent.

Step by step solution

01

Apply the given values.

The functions are y1(t)= 0, y2(t) = et

If the y1 and y2 are linearly dependent on the interval (0, 1) then

y1(t) = C1y2(t)

02

Find linearly dependent functions.

Now,

y1(t) = Cy2(t)

0 = Cet

C = 0

The value of C is a constant.

Therefore, these functions are linear dependent.

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