9780130084514

## Solution for problem 20 Chapter 1.5

# Let /, g, F(R, R) be the functions defined by f(t) = e rt and g(t) = e st , where r ^ s

Linear Algebra | 4th Edition

Problem 20

Let /, g, F(R, R) be the functions defined by f(t) = e rt and g(t) = e st , where r ^ s. Prove that / and g are linearly independent in J-(R, R)

**Accepted Solution**

Step-by-Step Solution:

Step 1 of 3

Given polynomial and , where .

Taylor expansion of as;

Taylor expansion of as;

###### Chapter 1.5, Problem 20 is Solved

**Step 2 of 3**

**Step 3 of 3**

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Let /, g, F(R, R) be the functions defined by f(t) = e rt and g(t) = e st , where r ^ s