Question

Ache o polinômio característico de A:​

Answer 1

$\large\boxed{\begin{array}{l}\sf \lambda\cdot I_2=\lambda\cdot\begin{bmatrix}\sf1&\sf0\\\sf0&\sf1\end{bmatrix}=\begin{bmatrix}\sf\lambda&\sf0\\\sf0&\sf\lambda\end{bmatrix}\\\\\sf \lambda\cdot I_2-A=\begin{bmatrix}\sf\lambda&\sf0\\\sf0&\sf\lambda\end{bmatrix}-\begin{bmatrix}\sf2&\sf-3\\\sf5&\sf1\end{bmatrix}\\\\\sf \lambda\cdot I_2-A=\begin{bmatrix}\sf\lambda-2&\sf3\\\sf\!\!-5&\sf\lambda-1\end{bmatrix}\\\\\sf p(\lambda)=det(\lambda\cdot I_2-A)\\\sf P(\lambda)=(\lambda-2)\cdot(\lambda-1)+15\end{array}}$

$\Large\boxed{\begin{array}{l}\sf p(\lambda)=\lambda^2-3\lambda+2+15\\\sf p(\lambda)=\lambda^2-3\lambda+17 \end{array}}$