Use matlab to find an invertible matrix p and a diagonal matrix d such that pdp-1 = f.


Exercise 4.4 (a) Let F- Use MATLAB to find an invertible matrix P and a diagonal matrix D such that PDr F (b) Use MATLAB to compare F10 and PD Op c) Let f= (1,1)T Compute Fr, Fr, F r FL Ft Describe the pattern in your answers. d) Given a sesquence of numbers ([.1.2.3.5,8. 13.) where each term is the sum of the previous two, find the 30th term of this sequence. if you are stuck., read the remark below) 13

Answer

Matlab code: ============== %%% part-a
f=[0 1;1 1]
[P D]=eig(f); % finding Eigenvalues and eigenvectors of f
P
D
P*D*P^-1 %%% part-b
F=f^10
P*D^10*P^-1 %%% part-c
f=[1 1]’;
F=[0 1;1 1];
F*f
F^2*f
F^3*f
F^4*f
F^5*f
% (F^n)*f gives the n+1 and n+2 term of fibonacci series %%% part-d
% required fibonacci term =30
% n+2=30 => n=28
F^28*f ================= Output: Editor G:Program Files MATLAB R2017alinMatx.m Ox Com mand Window >>linMatx 888 part-a f= [O [P D-eig (f); % finding Eigenval

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