Find Matrix P and the Diagonal Matrix D

  • Thread starter chwala
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  • #1
chwala
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Homework Statement
see attached - refer to part b only (part a was easy)
Relevant Equations
matrices
1712958779566.png


1712958822270.png


For part (b) i was able to use equations to determine the eigenvectors;

For example for ##λ =6##

##12x +5y -11z=0##
##8x-4z=0##
##32x+10y-26z=0## to give me the eigen vector,


##\begin{pmatrix}
1 \\
2 \\
2
\end{pmatrix}## and so on.

My question is to get matrix P does the arrangement of the eigenvector matrices matter?





1712959692049.png


In my arrangement for eigenvectors for ##λ=6,-4,2##

i have,

##P=\begin{pmatrix}
1 & 1& 1 \\
2 & 0 & -1 \\
2 & 2 & 1
\end{pmatrix}##

and my Diagonal matrix is

##D=\begin{pmatrix}
6^5 & 0 & 0 \\
0 & -4^5 & 0 \\
0 & 0 & 2^5
\end{pmatrix}=
\begin{pmatrix}
7776 & 0 & 0 \\
0 & -1024 & 0 \\
0 & 0 & 32
\end{pmatrix}
##
 
Last edited:
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  • #2
chwala said:
My question is to get matrix P does the arrangement of the eigenvector matrices matter?
No, but where you place the eigenvectors (i.e., in which columns) will determine P, which will determine ##P^{-1}## which will then determine where the eigenvalues appear on the diagonal matrix D.
 
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  • #3
Mark44 said:
No, but where you place the eigenvectors (i.e., in which columns) will determine P, which will determine ##P^{-1}## which will then determine where the eigenvalues appear on the diagonal matrix D.
Ok bass (boss). :wink: Gday @Mark44 :cool:
 
Last edited:

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