Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 9: Q2E (page 437)

Question: Solve the system
$\frac{d \overset{鈫�}{x}}{d t} = A \overset{鈫�}{x}$
for a 2x2 matrix A with complex eigenvalues $p 卤 i q$ .
2. Find $e^{\frac{1}{2} 蟺 i}$ .

Short Answer

Expert verified

Answer:

The solution is i.

Step by step solution

Euler’s formula

$e^{i t} = c o s t + i s i n t$

Explanation of the solution

To find the value of $e^{\frac{1}{2} 蟺 i}$ .

By using the Euler鈥檚 formula as follows.

$e^{i t} = c o s t + i s i n t e^{\frac{1}{2} 蟺 i} = c o s (\frac{蟺}{2}) + i s i n (\frac{蟺}{2}) e^{i \frac{1}{2} 蟺} = 0 + i e^{i \frac{1}{2} 蟺} = i$

Hence, the value of $e^{\frac{1}{2} 蟺 i}$ is i .

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91影视

Question: Solve the system
$\frac{d \overset{鈫�}{x}}{d t} = A \overset{鈫�}{x}$
for a 2x2 matrix A with complex eigenvalues $p 卤 i q$ .
2. Find $e^{\frac{1}{2} 蟺 i}$ .

Short Answer

Step by step solution

Euler’s formula

Explanation of the solution

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91影视

Question: Solve the systemdx鈫�dt=Ax鈫�for a 2x2 matrix A with complex eigenvaluesp卤iq.2. Finde12蟺i.

Short Answer

Step by step solution

Euler’s formula

Explanation of the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Logic and Functions

Pure Maths

Mechanics Maths

Statistics

Study anywhere. Anytime. Across all devices.

Question: Solve the system
$\frac{d \overset{鈫�}{x}}{d t} = A \overset{鈫�}{x}$
for a 2x2 matrix A with complex eigenvalues $p 卤 i q$ .
2. Find $e^{\frac{1}{2} 蟺 i}$ .