grandes-ecoles 2018 QI.4

grandes-ecoles · France · x-ens-maths__pc Matrices Determinant and Rank Computation
In this question only, we assume $n = 2$, and we denote $$I = \left(\begin{array}{ll} 1 & 1 \\ 1 & 1 \end{array}\right) \quad \text{and} \quad J = \left(\begin{array}{cc} 1 & 1 \\ 1 & -1 \end{array}\right)$$ Calculate $S(I)$ and $S(J)$, and deduce $S(A)$ for all $A \in \mathcal{M}_{2}(\{-1,1\})$. 
In this question only, we assume $n = 2$, and we denote
$$I = \left(\begin{array}{ll} 1 & 1 \\ 1 & 1 \end{array}\right) \quad \text{and} \quad J = \left(\begin{array}{cc} 1 & 1 \\ 1 & -1 \end{array}\right)$$
Calculate $S(I)$ and $S(J)$, and deduce $S(A)$ for all $A \in \mathcal{M}_{2}(\{-1,1\})$.
Paper Questions
QI.1 QI.2 QI.3 QI.4 QI.5 QI.6 QII.1 QII.2 QII.3 QII.4 QII.5 QII.6 QIII.1 QIII.2 QIII.3 QIII.4 QIV.1 QIV.2 QIV.3 QIV.4 QV.1 QV.2