grandes-ecoles 2011 QIV.B.1

grandes-ecoles · France · centrale-maths2__psi Not Maths

We consider four points $U_1, U_2, U_3, U_4$ in $\mathbb{R}^3$ satisfying $U_1U_2 = U_2U_3 = U_3U_4 = U_4U_1 = 1$, $U_1U_3 = a$ and $U_2U_4 = b$. We use the notations of the previous parts with $n = 4$.
We set $M = \left(\|U_i - U_j\|^2\right)_{(i,j) \in \llbracket 1,4\rrbracket^2} \in \mathcal{S}_4(\mathbb{R})$.
Write the matrix $M$ then calculate $S(M)$ and $\sigma(M)$.

We consider four points $U_1, U_2, U_3, U_4$ in $\mathbb{R}^3$ satisfying $U_1U_2 = U_2U_3 = U_3U_4 = U_4U_1 = 1$, $U_1U_3 = a$ and $U_2U_4 = b$. We use the notations of the previous parts with $n = 4$.

We set $M = \left(\|U_i - U_j\|^2\right)_{(i,j) \in \llbracket 1,4\rrbracket^2} \in \mathcal{S}_4(\mathbb{R})$.

Write the matrix $M$ then calculate $S(M)$ and $\sigma(M)$.

Paper Questions

QI.A QI.B QI.C QII.A QII.B QIII.A QIII.B QIV.A.1 QIV.A.2 QIV.A.3 QIV.B.1 QIV.B.2 QIV.B.3 QIV.B.4 QIV.B.5 QIV.B.6 QV.A.1 QV.A.2 QV.B.1 QV.B.2 QV.B.3 QV.C.1 QV.C.2 QV.C.3 QV.C.4 QV.C.5 QV.C.6 QV.C.7