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 1 & -1 \end{pmatrix}

Calculer M^2.

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

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

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

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

Calculer M^3.

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

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

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

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

Calculer M^4.

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

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

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

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