Can someone help me explain how to solve this problem below:
Let the matrix $\mathbf{A}$ be given as $$\mathbf{A}=\begin{bmatrix}0&-1&-1\\1&2&1\\1&1&2\end{bmatrix}$$
1. Compute the characteristic equation.
Would something like this be correct?
$$(\lambda-2)(\lambda-2)(\lambda-0)-\ldots$$
But I'm not sure.
Best Answer
The easy and quick way to compute the characteristic equation of 3x3 matrix is to use the formulae $$x^3-tr(A)x^2+(A_{11}+A_{22}+A_{33})x-det(A)=0$$ For given matrix $$tr(A)=4, A_{11}(cofa_{11})=3, A_{22}(cofa_{22})=1, A_{33}(cofa_{33})=1, det(A)=2$$ so the char equation will be $x^3-4x^2+5x-2=0$