Calculer la puissance d'une matrice dans un cas simple Exercice

On considère la matrice carrée d'ordre 2 suivante :

M=\begin{pmatrix} -1 & 1 \cr\cr 2 & -2 \end{pmatrix}

Calculer M^2.

M^2 =\begin{pmatrix} 3& −3\cr\cr −6& 6\end{pmatrix}

M^2 =\begin{pmatrix} 3& 3\cr\cr −6& 6\end{pmatrix}

M^2 =\begin{pmatrix} 3& −3\cr\cr 6& 6\end{pmatrix}

M^2 =\begin{pmatrix} −3& −3\cr\cr −6& 6\end{pmatrix}

Calculer M^3.

M^3 = \begin{pmatrix} −9& 9\cr\cr 18&−18\end{pmatrix}

M^3 = \begin{pmatrix} 9& 9\cr\cr 18&−18\end{pmatrix}

M^3 = \begin{pmatrix} −9& 9\cr\cr 18&18\end{pmatrix}

M^3 = \begin{pmatrix} −9& −9\cr\cr 18&−18\end{pmatrix}

Calculer M^4.

M^4 = \begin{pmatrix} 27& −27\cr\cr −54& 54\end{pmatrix}

M^4 = \begin{pmatrix} 27& 27\cr\cr −54& 54\end{pmatrix}

M^4 = \begin{pmatrix} 27& −27\cr\cr 54& 54\end{pmatrix}

M^4 = \begin{pmatrix} −27& −27\cr\cr −54& 54\end{pmatrix}