Respuesta :
P=⎡1 1 5
−3 0 -1
1 1 1⎤ is the required matrix.
Since, P is matrix of eigenvectors of A. You find the eigenvectors by solving the equation (λI−A)x=0
For eigenvalue λ=0, the eigenvector is ⎡1
−3
1⎤
For eigenvalue λ=−3, the eigenvector ⎡1
0
1⎤
For eigenvalue λ=1, the associated eigenvector ⎡5
−1
1⎤
Hence, P=⎡1 1 5
−3 0 -1
1 1 1⎤
The question is incomplete, here you can find a complete question A matrix is
A=⎡−5 2 −6
−1 0 −1
2 −2 3⎤, and I need to find an invertible matrix P and a diagonal matrix D such that D=P⁻¹AP. The eigenvalues for the matrix are −3, 1, 0,
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