1. What is an eigenvector?2. Find the eigenvectors of the following matrices.(a)21[0(b)-1 1-1(c)1 13. 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 212+3 (Y? - 4Y)(c) Y+15. Find the equilibria of the following differential equations.(a) mx"(t) ax' (t)+ kx(t) = 0y(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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Asked Sep 3, 2019
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I need help for problem 5c. Thanks!

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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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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Expert Answer

Step 1

(c)

Consider the given differential equation:

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N'() N()

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Step 2

Now, it is known that the equilibria of a differential equation is eval...

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N(t) 0 AN()0 N (t) 0

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