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
A =
1 1 1
2 1 1
8 5 3
- Find the eigenvalues and eigenvectors ofA. Denote eigenvalues as 1 , 2 , 3 and eigenvectors asv 1 ,v 2 ,v 3.
- 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
- 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
3
2
2
+c 2 et
2
1
0
+c 3 e^5 t
2
3
1
(1)
wherec 1 ,c 2 andc 3 are arbitrary constants.
- What are the eigenvalues and eigenvectors ofA?
- IsAdiagonalizable?
- Find a matrixAso that the general solution ofx=Axis (1).
Problem 3:Find the general solution of the following equation.
x =
[
3 2
2 3
]
x.
Problem 4:Solve the following initial value problem
x =
1 1 0
0 1 4
0 4 1
x, x(0) =
1
2
1
.
1
Problem 5:Find the general solution to the following equations.
x =
[
1 3
3 7
]
x.
Problem 6:Find the general solution to the following equation.
x =
0 1 0 0. 5
4 0 2 0
0 0 0 1
0 0 4 0
x.
(The eigenvalues of the coefficient matrix are 1 = 2 = 2i, 3 = 4 = 2 i.)
Problem 7:Let
A =
3 0 2
2 1 1
0 0 1
.
The eigenvalues ofAare 1 = 3, 2 = 3 = 1. Solve the initial value problem:
x = Ax, x(0) =