(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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]

2. Relevant equations

3. 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?

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# Homework Help: Linear Algebra - Characteristic polynomials and similar matrices question

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