# 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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I need help for problem 5c. Thanks!

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Step 1

(c)

Consider the given differential equation:

Step 2

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

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