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Eigenvalues and eigenspaces/-4 6 6 0 2 0 -3 3 5/Exercise
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Let
A
=
(
−
4
6
6
0
2
0
−
3
3
5
)
∈
Mat
3
×
3
(
R
)
.
{\displaystyle {}A={\begin{pmatrix}-4&6&6\\0&2&0\\-3&3&5\end{pmatrix}}\in \operatorname {Mat} _{3\times 3}(\mathbb {R} )\,.}
Compute:
the eigenvalues of
A
{\displaystyle {}A}
;
the corresponding eigenspaces;
the geometric and algebraic multiplicities of each eigenvalue;
a matrix
C
∈
Mat
3
×
3
(
R
)
{\displaystyle {}C\in \operatorname {Mat} _{3\times 3}(\mathbb {R} )}
such that
C
−
1
A
C
{\displaystyle {}C^{-1}AC}
is a diagonal matrix.
Create a solution