- #1

chwala

Gold Member

- 2,666

- 352

- Homework Statement
- see attached - refer to part b only (part a was easy)

- Relevant Equations
- matrices

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?

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: