So far I've found the characteristic equation.

[Math] (t-1)^2(t+2) [/tex]

So the eigenvalues, are $\displaystyle 1,1,-2$

And I know the jordan matrix is along these lines(below)

$\displaystyle J= \begin{bmatrix}1&0&0\\0&1&0\\0&0&-2\end{bmatrix} $

But I literally have

__NO__ clue on where the extra 1's should be.

I know a singular eigenvector towards T for sure, but I'm confused on -2, as the answer is totally different in my mark scheme :S!

so.....

$\displaystyle \textit{}

e^1 =

\left( {\begin{array}{cc}

1 \\

1 \\

1

\end{array} } \right)$

$\displaystyle \textit{}

e^{-2} =

\left( {\begin{array}{cc}

2 \\

1 \\

1

\end{array} } \right)$

For the last one i'm trying...

[Math](A-I)^2\begin{bmatrix}a&b&c\end{bmatrix}=\begin{bmatr ix}1&1&1\end{bmatrix}[/tex]

$\displaystyle T= \begin{bmatrix}1&2&e^1\\1&1&e^1\\1&1&e^1}\end{bmat rix} $

I also know $\displaystyle A^5 = TJ^5T^{-1}$

I know this is a bit scrappy but could anybody help me on the bits i'm struggling with..

1) Finding a second eigenvector for t=1, making sure my t=-2 eigenvector is correct.

2) Explaining how you decide how many, and where to put the 1's in a jordan matrix.

Thank you