1. What is an eigenvector? 2. Find the eigenvectors of the following matrices. (a) 2 1 [ 0 (b) -1 1 -1 (c) 1 1 3. What is a fixed point of a function? 4. Find the fixed points of the following discrete time difference equations. (a) Nt+1 (1+rN) Nt (b) Xt+1 (1 + X) Xt 2 12+3 (Y? - 4Y) (c) Y+1 5. Find the equilibria of the following differential equations. (a) mx"(t) ax' (t)+ kx(t) = 0 y(t) 1 (b) y'(t) ry(t) K (c) N'(t) AN (t) 6. Bonus: for each of the differential equations above, how do values of y(t) (or x(t) fixed points "behave"? (i.e. are they moving towards or away from the fixed points?) or N(t))near the
1. What is an eigenvector? 2. Find the eigenvectors of the following matrices. (a) 2 1 [ 0 (b) -1 1 -1 (c) 1 1 3. What is a fixed point of a function? 4. Find the fixed points of the following discrete time difference equations. (a) Nt+1 (1+rN) Nt (b) Xt+1 (1 + X) Xt 2 12+3 (Y? - 4Y) (c) Y+1 5. Find the equilibria of the following differential equations. (a) mx"(t) ax' (t)+ kx(t) = 0 y(t) 1 (b) y'(t) ry(t) K (c) N'(t) AN (t) 6. Bonus: for each of the differential equations above, how do values of y(t) (or x(t) fixed points "behave"? (i.e. are they moving towards or away from the fixed points?) or N(t))near the
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Please help me solve problem 5b. Thanks!
Transcribed Image Text:1. What is an eigenvector?
2. Find the eigenvectors of the following matrices.
(a)
2
1
[
0
(b)
-1 1
-1
(c)
1 1
3. What is a fixed point of a function?
4. Find the fixed points of the following discrete time difference equations.
(a) Nt+1 (1+rN) Nt
(b) Xt+1 (1 + X) Xt 2
12+3 (Y? - 4Y)
(c) Y+1
5. Find the equilibria of the following differential equations.
(a) mx"(t) ax' (t)+ kx(t) = 0
y(t)
1
(b) y'(t) ry(t)
K
(c) N'(t) AN (t)
6. Bonus: for each of the differential equations above, how do values of y(t) (or x(t)
fixed points "behave"? (i.e. are they moving towards or away from the fixed points?)
or N(t))near the
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