×
Get Full Access to Precalculus Enhanced With Graphing Utilities - 6 Edition - Chapter 5.4 - Problem 129
Get Full Access to Precalculus Enhanced With Graphing Utilities - 6 Edition - Chapter 5.4 - Problem 129

×

# 127130 use the following discussion: The loudness L(x),

ISBN: 9780132854351 232

## Solution for problem 129 Chapter 5.4

Precalculus Enhanced with Graphing Utilities | 6th Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants

Precalculus Enhanced with Graphing Utilities | 6th Edition

4 5 1 354 Reviews
10
1
Problem 129

127130 use the following discussion: The loudness L(x), measured in decibels (dB), of a sound of intensity x, measured in watts per square meter, is defined as L(x) = 10 log x I0 , where I0 = 10-12 watt per square meter is the least intense sound that a human ear can detect. Determine the loudness, in decibels, of each of the following sounds

Step-by-Step Solution:
Step 1 of 3

4.5 Complex Eigenvalues/Eigenvectors Recall: • Complex eigenvalues always have complex eigenvectors. • Complex eigenvalues occur in conjugate pairs. • Definition: Au= u λhere A is the matrix, u is the nonzero eigenvector associated with the eigenvalue, λ . There are always infinitely many eigenvectors for each eigenvalue. These eigenvectors are multiples of each other. One problem that arises when dealing with complex vectors is that it is difficult to recognize multiples. We have to perform complex arithmetic to see if vectors are multiples. ⎡ 1 ⎤ ⎡ 2 ⎤ ⎡ 5 ⎤ We can easily tell that ⎢ 2 ⎥ , ⎢ 4 ⎥ and ⎢ 10 ⎥ are multiples. ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎡ i +1 ⎤ ⎡ −1+i ⎤ ⎡ 1+ 3i ⎤ It is difficult, however to recognize that ⎢ ⎥, ⎢ ⎥ and ⎢ ⎥ ⎣ 2i − 3 ⎦ ⎣ −2 − 3i ⎦ ⎣ −8 +i ⎦ ⎡ i +1 ⎤ ⎡ −1+i ⎤ are multiples. But if we check i ⎢ ⎥ = ⎢ ⎥ ⎣ 2i − 3 ⎦ ⎣ −2 − 3i ⎦ and if we check (2+i) ⎡ i +1 ⎤ = ⎡ 1+ 3i ⎤. ⎣ 2i − 3 ⎦ ⎣ −8 +i ⎦ To find eigenvalues, solve det(A- I) λ 0. To find corresponding eigenvectors, reduce [A- I | 0]λ What if we’re given an eigenvector and a matrix and asked for the eigenvalue The above isn’t our only option.

Step 2 of 3

Step 3 of 3

## Discover and learn what students are asking

#### Related chapters

Unlock Textbook Solution