Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Fibonacci sequence. The Fibonacci sequence yo, y1, Y2₂, ... starts with yo = 0, y₁ = 1, and for t = 2, 3,..., Yt Yt-1+Yt-2, i.e., the sum of the previous two entries. (a) Express this as a time-invariant linear dynamical system with state xt = t = 1,2,.... That is, find A and C, where Xt+1 = Axt and Yt = Cxt. (yt, Yt-1) and output yt, for (b) Use your matrix expression above and MATLAB to compute and plot the Fibonacci sequence y, for t = 0, ..., 20. (c) Using MATLAB, simulate a modified Fibonacci sequence Zo, Z₁, Z2, ..., which starts with the same = 1, but for t = 2, 3,..., values Zo = 0 and Z₁ Zt Zt-1 Zt-2, i.e., the difference of the two previous values. Plot this sequence z, for t = 0, ..., 20.

Fibonacci sequence. The Fibonacci sequence yo, y1, Y2₂, ... starts with yo = 0, y₁ = 1, and for t = 2, 3,..., Yt Yt-1+Yt-2, i.e., the sum of the previous two entries. (a) Express this as a time-invariant linear dynamical system with state xt = t = 1,2,.... That is, find A and C, where Xt+1 = Axt and Yt = Cxt. (yt, Yt-1) and output yt, for (b) Use your matrix expression above and MATLAB to compute and plot the Fibonacci sequence y, for t = 0, ..., 20. (c) Using MATLAB, simulate a modified Fibonacci sequence Zo, Z₁, Z2, ..., which starts with the same = 1, but for t = 2, 3,..., values Zo = 0 and Z₁ Zt Zt-1 Zt-2, i.e., the difference of the two previous values. Plot this sequence z, for t = 0, ..., 20.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.5: Systems Of Linear Equations In More Than Two Variables
Problem 27E
See similar textbooks
icon
Related questions
Question
Fibonacci sequence. The Fibonacci sequence yo, y₁, y2, ... starts with yo = 0, y₁ = 1, and for t = 2, 3, ..., Yt = Yt-1+Yt-2, i.e., the sum of the previous two entries. (a) Express this as a time-invariant linear dynamical system with state x₁ = (yt, Yt-1) and output yt, for t = 1, 2,.... That is, find A and C, where Xt+1 = Axt and Yt = Cxt. (b) Use your matrix expression above and MATLAB to compute and plot the Fibonacci sequence yt for t = 0,..., 20. (c) Using MATLAB, simulate a modified Fibonacci sequence Zo, Z₁, Z2, ..., which starts with the same : 1, but for t = 2, 3,..., values Zo = 0 and Z₁ = Zt Zt-1-Zt-2, = i.e., the difference of the two previous values. Plot this sequence z, for t = 0,..., 20.
Transcribed Image Text:Fibonacci sequence. The Fibonacci sequence yo, y₁, y2, ... starts with yo = 0, y₁ = 1, and for t = 2, 3, ..., Yt = Yt-1+Yt-2, i.e., the sum of the previous two entries. (a) Express this as a time-invariant linear dynamical system with state x₁ = (yt, Yt-1) and output yt, for t = 1, 2,.... That is, find A and C, where Xt+1 = Axt and Yt = Cxt. (b) Use your matrix expression above and MATLAB to compute and plot the Fibonacci sequence yt for t = 0,..., 20. (c) Using MATLAB, simulate a modified Fibonacci sequence Zo, Z₁, Z2, ..., which starts with the same : 1, but for t = 2, 3,..., values Zo = 0 and Z₁ = Zt Zt-1-Zt-2, = i.e., the difference of the two previous values. Plot this sequence z, for t = 0,..., 20.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 41 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
SEE MORE TEXTBOOKS