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zeion
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Homework Statement
For each matrix A below, let T be the linear operator on R3 thathas matrix A relative to the basis A = {(1,0,0), (1,1,0), (1,1,1)}. Find the algebraic and geometric multiplicities of each eigenvalues, and a basis for each eigenspace.
a) A = [tex]
\begin{bmatrix} 8&5&-5\\5&8&-5\\15&15&-12\end{bmatrix}
[/tex]
Homework Equations
The Attempt at a Solution
So I tried to find the eigenvalues normally and turns out that was pretty hard.. So I know that similar matrices have the same eigenvalues, then can I just take the eigenvalues of the matrix [tex]
\begin{bmatrix} 1&1&1\\0&1&1\\0&0&1\end{bmatrix}
[/tex]
since it is similar to A? Or is it similar?