# I need help with the second part of this problem.

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• Dec 11th 2007, 02:27 PM
Ral
I need help with the second part of this problem.
http://img409.imageshack.us/img409/2644/matrixnh4.jpg
A.) Determine the characteristic polynomial and characteristic roots of A.

For this, I got $X^2-6X+8$ and Roots: X=4 and X=2

I'm not sure what to do for the next part.
B.) Find a nonsingular matrix P and diagonal matrix D such that $P^{-1}*AP= D$.
• Dec 12th 2007, 03:23 AM
badgerigar
D = $\begin {pmatrix} 2 & 0 \\ 0 & 4\end{pmatrix}$ or $\begin {pmatrix} 4 & 0 \\ 0 & 2\end{pmatrix}$

Since each of the roots of the characteristic equation have multiplicity 1, we can tell that the matrix is similar to any matrix with those roots on the diagonal and 0s elsewhere.