  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

Question

I need help for problem 2b. Thanks help_outlineImage Transcriptionclose1. 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 fullscreen
Step 1

Given: -

Step 2

To calculate: -

Eigen vectors of the given matrix.

Step 3

Calculation... help_outlineImage TranscriptioncloseFinding the characteristic equation that is, |A -AI from the given matrix So, 1 0 1 0 (A-I) 1 0 1 0 -2 1 -1 1- 0 A -2. 1 =(-2)(1-)-(-1) = -2+22 +1 -1 1-2 A-A=22-2+1 (1) Now, putting (1) equals to 0, then 2-2+1 0 1+3i 1-3i 2 2 fullscreen

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