2)A)

find the definative polinomial and the minimal polinomial of

$\displaystyle A=\left(\begin{array}{ccc}3 & 1 & -1\\2 & 2 & 0\\1 & -1 & 3\end{array}\right)$

find the primary decomposition of $\displaystyle R^{3}$ in this case,and write the diagonal block matrices

similar to A

?

B)

find the jordan form of A defined in part A

and find the transformation matrices to the basis for which it represented in jordan form.

how i tried:

regarding A:

how i tried:

|tI-A|=$\displaystyle \left|\begin{array}{ccc}t-3 & -1 & +1\\-2 & t-2 & 0\\-1 & 1 & t-3\end{array}\right|$=$\displaystyle 1\left|\begin{array}{cc}-2 & t-2\\-1 & 1\end{array}\right|+0+(t-3)\left|\begin{array}{cc}t-3 & -1\\-2 & t-2\end{array}\right|$=$\displaystyle -2+t-2+(t-3)[(t-3)(t-2)+2]=t-4+(t-3)[t^{2}-2t-3t+6+2]$=$\displaystyle t-4+(t-3)[t^{2}-5t+8]$

=$\displaystyle t-4+t^{3}-5t^{2}+8t-3t^{2}+15t-24=t^{3}-8t^{2}+24t-28$

there are some roots possible by theory t=1,-1,+28,-28

t=1: 1-8+24-28

t=-1: -1-8-24-28

from the calculator the other dont work too

??