Chapter 4: Q28E (page 164)

In Problems 27–32, use Definition 1 to determine whether the functions y₁and y₂are linearly dependent on the interval (0, 1).
28. y₁(t) = e^3t, y₂(t) = e^-4t

Short Answer

Expert verified

The functions are not linearly dependent.

Step by step solution

Apply the given values.

The given functions are y₁(t) = e^3t, y₂(t) = e^-4t

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

y₁(t) = C₁y₂(t)

Find linearly dependent functions.

Now,

$e^{3 t} \neq C e^{- 4 t}$

This cannot be expressed as e^3t multiples of e^-4t.

Therefore, these functions are not linear dependent.

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In Problems 27–32, use Definition 1 to determine whether the functions y₁and y₂are linearly dependent on the interval (0, 1).
28. y₁(t) = e^3t, y₂(t) = e^-4t

Short Answer

Step by step solution

Apply the given values.

Find linearly dependent functions.

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In Problems 27–32, use Definition 1 to determine whether the functions y1and y2are linearly dependent on the interval (0, 1).28. y1(t) = e3t, y2(t) = e-4t

Short Answer

Step by step solution

Apply the given values.

Find linearly dependent functions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Statistics

Mechanics Maths

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 27–32, use Definition 1 to determine whether the functions y₁and y₂are linearly dependent on the interval (0, 1).
28. y₁(t) = e^3t, y₂(t) = e^-4t