- #1
mpittma1
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Homework Statement
Find a Matrix P that diagonalizes A
Homework Equations
A = [tex]
\begin{pmatrix}
2 & 0 & -2\\
0 & 3 & 0\\
0 & 0 & 3
\end{pmatrix}
[/tex]
The Attempt at a Solution
Well right off the bat we know that this is an upper triangular matrix so the eigenvalues are the entries along the main diagonal of A.
So λ = 2, 3, 3
But if an n x n matrix A has n distinct eigenvalues, then A is diagonalizable.
In this case we only have 2 distinct eigenvalue so it shouldn't be diagonalizable...
But the answer is:
P = [tex]
\begin{pmatrix}
-2 & 0 & 1\\
0 & 1 & 0\\
1 & 0 & 0
\end{pmatrix}
[/tex]
What is the proper way to start the problem to find this matrix P?
Thank You for any help in advance.