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Eigenvalues and eigenspaces/-5 0 7 6 2 -6 -4 0 6/Exercise
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Let
A
=
(
−
5
0
7
6
2
−
6
−
4
0
6
)
∈
Mat
3
×
3
(
R
)
.
{\displaystyle {}A={\begin{pmatrix}-5&0&7\\6&2&-6\\-4&0&6\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.
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