So I was able to find eigenvalue and eigenvector for given matrix A. my question

Question

So I was able to find eigenvalue and eigenvector for given matrix A. my question is I do not have any idea how to approach to solve 10 and 11. for 10 is to give out Eigenvalue Diagonalization, but my Matlab give out different answers after computing i get

0.3820 -0.0000 0.0000 -0.0000
-0.0000 1.3820 -0.0000 -0.0000
-0.0000 0.0000 2.6180 -0.0000
-0.0000 -0.0000 -0.0000 3.6180

as my diagonalization matrix. But Correct answer is  

I only got diagonals right but not the other values please help. Also this is the same situtaion for my Triple Product. Please help me with detail answers and solutions!

0.381966011 1.80411E-16 -2.63678E-16 -9.50628E-16 0 1.381966011 9.99201E-16 -9.4369E-16 0 -1.11022E-16 2.618033989 -3.33067E-16 4.44089E-16 -2.22045E-16 3.33067E-16 3.618033989 -1 [A] = size (4,4) -1 -1 -1 -1 -1

Explanation / Answer

clc
clear all

Matlab code

format long
A=[2 -1 0 0;-1 2 -1 0;0 -1 2 -1;0 0 -1 2];
[phi,lambda] = eig(A)
k=inv(phi)*A*phi
k1=inv(phi)*eye(4,4)*phi
k2=(phi)'*A*phi
k3=(phi)'*eye(4,4)*phi

"I only got diagonals right but not the other values please help. Also this is the same situtaion for my Triple Product. Please help me with detail answers and solutions!"

Actually you got all the values right,it is under precision of your machine.It was same case for me."formatlongEng" will give the long output.

Output after introducing formatlongEng

phi =

371.748034460185e-003 -601.500955007546e-003 -601.500955007546e-003 -371.748034460185e-003
601.500955007546e-003 -371.748034460185e-003 371.748034460185e-003 601.500955007546e-003
601.500955007545e-003 371.748034460184e-003 371.748034460184e-003 -601.500955007545e-003
371.748034460184e-003 601.500955007545e-003 -601.500955007545e-003 371.748034460185e-003

lambda =

381.966011250105e-003 0.00000000000000e+000 0.00000000000000e+000 0.00000000000000e+000
0.00000000000000e+000 1.38196601125011e+000 0.00000000000000e+000 0.00000000000000e+000
0.00000000000000e+000 0.00000000000000e+000 2.61803398874989e+000 0.00000000000000e+000
0.00000000000000e+000 0.00000000000000e+000 0.00000000000000e+000 3.61803398874989e+000

k =

381.966011250105e-003 180.411241501588e-018 -263.677968348475e-018 -950.628464835290e-018
0.00000000000000e+000 1.38196601125011e+000 999.200722162641e-018 -943.689570931383e-018
0.00000000000000e+000 -111.022302462516e-018 2.61803398874990e+000 -333.066907387547e-018
444.089209850063e-018 -222.044604925031e-018 333.066907387547e-018 3.61803398874990e+000

k1 =

1.00000000000000e+000 83.2667268468867e-018 -27.7555756156289e-018 -222.044604925031e-018
27.7555756156289e-018 1.00000000000000e+000 333.066907387547e-018 -111.022302462516e-018
-27.7555756156289e-018 -55.5111512312578e-018 1.00000000000000e+000 -27.7555756156289e-018
0.00000000000000e+000 27.7555756156289e-018 -27.7555756156289e-018 1.00000000000000e+000

k2 =

381.966011250105e-003 -319.189119579733e-018 83.2667268468867e-018 409.394740330526e-018
-333.066907387547e-018 1.38196601125010e+000 55.5111512312578e-018 55.5111512312578e-018
0.00000000000000e+000 -111.022302462516e-018 2.61803398874989e+000 999.200722162641e-018
666.133814775094e-018 222.044604925031e-018 888.178419700125e-018 3.61803398874989e+000

k3 =

1.00000000000000e+000 -277.555756156289e-018 111.022302462516e-018 194.289029309402e-018
-277.555756156289e-018 1.00000000000000e+000 -55.5111512312578e-018 166.533453693773e-018
111.022302462516e-018 -55.5111512312578e-018 1.00000000000000e+000 194.289029309402e-018
194.289029309402e-018 166.533453693773e-018 194.289029309402e-018 1.00000000000000e+000

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