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

On considère la matrice carrée d'ordre 2 suivante :

M=\begin{pmatrix} -2 & 0 \cr\cr 1 & 2 \end{pmatrix}

Calculer M^2.

M^2 =\begin{pmatrix} 4& 0\cr\cr 0& 4\end{pmatrix}

M^2 =\begin{pmatrix} −4& 0\cr\cr 0& −4\end{pmatrix}

M^2 =\begin{pmatrix} 0 & 4\cr\cr 4& 0\end{pmatrix}

M^2 =\begin{pmatrix} 0& −4\cr\cr −4& 0\end{pmatrix}

Calculer M^3.

M^3 = \begin{pmatrix} −8& 0\cr\cr 4&8\end{pmatrix}

M^3 = \begin{pmatrix} 8& 0\cr\cr 4&8\end{pmatrix}

M^3 = \begin{pmatrix} −8& 0\cr\cr 8&4\end{pmatrix}

M^3 = \begin{pmatrix} 8& 0\cr\cr 8&4\end{pmatrix}

Calculer M^4.

M^4 = \begin{pmatrix} 16& 0\cr\cr 0& 16\end{pmatrix}

M^4 = \begin{pmatrix} −16& 0\cr\cr 0& −16\end{pmatrix}

M^4 = \begin{pmatrix} 8& 0\cr\cr 0& 8\end{pmatrix}

M^4 = \begin{pmatrix} −8& 0\cr\cr 0& −8\end{pmatrix}