\( \left\{\begin{array}{c}3 x-2 y-z=11 \\ 2 x-5 y-2 z=3 \\ -5 x-y+2 z=-33\end{array}\right. \) b) \( \left\{\begin{array}{c}x+2 y-6 z=4 \\ 2 x-2 y+3 z=4 \\ x+8 y-21 z=6\end{array}\right. \)

considère les matrices suivantes de \( \mathcal{M}_{3}(\mathrm{R}): \mathrm{M}=\left(\begin{array}{lll}0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array}\right) \) et \( \mathrm{J}=\mathrm{M}+\mathrm{I}_{3} \). Calculer \( J^{2}, J^{3} \) (On admettra dans la suite que \( \left.\forall k \in \mathrm{~N}^{*}, J^{k}=3^{k-1} J\right) \) En remarquant que \( \mathrm{M}=\mathrm{J}-\mathrm{I}_{3} \), démontrer que, pour tout \( \mathrm{n} \in \mathrm{N}, \mathrm{M}^{\mathrm{n}}=(-1)^{\mathrm{n}} \mathrm{I}_{3}+\frac{1}{3}\left(2^{\mathrm{n}}-(-1)^{\mathrm{n}}\right) \mathrm{J} \).

Oppgave \( 9(1+1+2+2 \) poe Los likningene. a) \( \quad x-10=10 \)

Multiply. \( \begin{array}{ll}\left(7 x^{2}\right)\left(-9 x^{2}\right)\left(2 x^{3}\right) \\ & \left(7 x^{2}\right)\left(-9 x^{2}\right)\left(2 x^{3}\right)=\square \\ & \text { Simplify your answer.) }\end{array} \)

b) \( x-10=2 x+4 \quad \) Svan

a) \( 4 x+y=2 \) b) \( 4 x+2 x-2 y=3+1 \)