convert it into a diagonal matrix. all the leading diagonal elements form the eigenvalues.
Find the eigenvalues for the following matrix:
A=
1 2 2 2
2 1 2 2
2 2 1 2
2 2 2 1
det(A-λI)=
1-λ 2 2 2
2 1-λ 2 2
2 2 1-λ 2
2 2 2 1-λ
Is there a shortcut to computing this? Or do I need to take (1-λ)det(3x3 matrix)-(2)det(3x3 matrix)+(2)det(3x3 matrix)-(2)det(3x3 matrix)?