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diagonalize (
6
−1
2
3
)
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Solution
P=(
1
1
1
2
),D=(
5
0
0
4
),P−1=(
2
−1
−1
1
)
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Solution steps
Solve by:
One step at a time
(
6
−1
2
3
)
Matrix diagonalization
A matrix A can be diagonalized if there exists an invertible matrix P and diagonal matrix D such that A=PDP−1
Find the eigenvalues for (
6
−1
2
3
):λ=5,λ=4
The diagonal matrix D is composed of the Eigenvalues:
D=(
5
0
0
4
)
Find the eigenvectors for (
6
−1
2
3
):(
1
1
),(
1
2
)
The Eigenvectors corresponding to the Eigenvalues in D compose the columns of P :