# matlab | lab – AM 20 Week 7 Homework

### AM 20 Week 7 Homework

matlab | lab – 该题目是一个常规的matlab的练习题目代写, 涵盖了matlab等方面, 这个项目是lab代写的代写题目

Problem 1:Consider the equationx = Ax. where

#### 8 5 3

1. Find the eigenvalues and eigenvectors ofA. Denote eigenvalues as 1 , 2 , 3 and eigenvectors asv 1 ,v 2 ,v 3.
2. LetP= [v 1 ,v 2 ,v 3 ] andy(t) =P^1 x(t). Show that
``````y =
``````
`````` 1 0 0
0  2 0
0 0  3
``````
``````y
``````
1. Find the general solution ofyand the general solution ofx. (You can Use mat lab command [V,D]=eig(A,nobalance) to help you with the eigen- value/eigenvector computation.)

Problem 2: LetAbe a 33 constant matrix. Suppose the general solution of x=Ax,xR^3 , is

``````x(t) = c 1 et
``````

#### 2

``````+c 2 et
``````

#### 0

``````+c 3 e^5 t
``````

#### (1)

wherec 1 ,c 2 andc 3 are arbitrary constants.

1. What are the eigenvalues and eigenvectors ofA?
3. Find a matrixAso that the general solution ofx=Axis (1).

Problem 3:Find the general solution of the following equation.

``````x =
``````

#### ]

``````x.
``````

Problem 4:Solve the following initial value problem

``````x =
``````

#### 0 4 1

``````x, x(0) =
``````

#### 1

Problem 5:Find the general solution to the following equations.

``````x =
``````

#### ]

``````x.
``````

Problem 6:Find the general solution to the following equation.

``````x =
``````

#### 0 0 4 0

``````x.
``````

(The eigenvalues of the coefficient matrix are 1 = 2 = 2i, 3 = 4 = 2 i.)

Problem 7:Let

#### .

The eigenvalues ofAare 1 = 3, 2 = 3 = 1. Solve the initial value problem:

``````x = Ax, x(0) =
``````