Example of repeated eigenvalues, Mathematics

Assignment Help:

Illustration: Solve the following IVP.

1016_Example of Repeated eigenvalues.png

Solution:

First get the eigenvalues for the system.

1604_Example of Repeated eigenvalues1.png

= l2 - 10 l+ 25

= (l- 5)2

l1,2 = 5

Therefore, we got a double eigenvalue. Obviously that must not be too surprising given the section which we're in. here we find the eigenvector for that eigenvalue.

704_Example of Repeated eigenvalues2.png

2h1 +   h2 = 0,                         ⇒         h2 = - 2h1

446_Example of Repeated eigenvalues3.png

The eigenvector is,

h1≠ 0

h1= 1

The next step is get ?r.  To do this we'll require solving,

848_Example of Repeated eigenvalues4.png

2  ?r1+  ?r2 = 1,                       ?r2 = 1 - 2  ?r1

Remember that this is almost the same to the system which we solve to find the eigenvalue.  The simple difference is the right hand side. The most common possible ?r is,

601_Example of Repeated eigenvalues5.png

If r1 = 0

During this case, unlike the eigenvector system we can select the constant to be anything we need, therefore we might as well pick it to create our life easier. This generally means picking this to be zero.

 We can now write down the general solution to the system.

109_Example of Repeated eigenvalues6.png

Applying the initial condition to get the constants provides us,

2087_Example of Repeated eigenvalues7.png

c1 = 2;

-2 c1 + c2 = -5;

By solving both equations we get:

c1 = 2;

c2 = -1

The actual solution is,

1353_Example of Repeated eigenvalues8.png


Related Discussions:- Example of repeated eigenvalues

Fractions, what Is the common denominator for 1/2 and 1/4

what Is the common denominator for 1/2 and 1/4

.., rectangles 7cm by 4cm

rectangles 7cm by 4cm

One tailed test, One Tailed Test It is a test where the alternative hy...

One Tailed Test It is a test where the alternative hypothesis (H 1 :) is only concerned along with one of the tails of the distribution for illustration, to test a business co

Help me help me!, A 65 ohm resistor is connected to a power supply , a curr...

A 65 ohm resistor is connected to a power supply , a current of 2.4 amperes is drawn. what is the output voltage?

Formula to calculate the surface area of basketball, Keith wants to know th...

Keith wants to know the surface area of a basketball. Which formula will he use? The surface area of a sphere is four times π times the radius squared.

Describe adding and subtracting square roots, Describe Adding and Subtracti...

Describe Adding and Subtracting Square Roots? To add or subtract square roots, the radicands must be the same. If the radicands are the same, add/subtract the coefficients (the

What is the average temperature on the celsius scale, Peggy's town has an a...

Peggy's town has an average temperature of 23° Fahrenheit in the winter. What is the average temperature on the Celsius scale? If the total amount for both is 80, after that th

Fractions, my daughter brought home home work im not sure how to do it the ...

my daughter brought home home work im not sure how to do it the fractions has to be labled from least to greatest

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd