Find the characteristic polynomial of A=[100020003]A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{bmatrix}A=100020003
p(λ)=(1−λ)(2−λ)(3−λ)p(\lambda) = (1-\lambda)(2-\lambda)(3-\lambda)p(λ)=(1−λ)(2−λ)(3−λ)
p(λ)=λ3−6λ2+11λ−6p(\lambda) = \lambda^3 - 6\lambda^2 + 11\lambda - 6p(λ)=λ3−6λ2+11λ−6
p(λ)=(λ−1)(λ−2)(λ−3)p(\lambda) = (\lambda-1)(\lambda-2)(\lambda-3)p(λ)=(λ−1)(λ−2)(λ−3)
p(λ)=λ3−3λ+6p(\lambda) = \lambda^3 - 3\lambda + 6p(λ)=λ3−3λ+6