grandes-ecoles 2013 QIII.D.1

grandes-ecoles · France · centrale-maths2__pc Invariant lines and eigenvalues and vectors Geometric interpretation of eigenstructure

For $A = \left(\begin{array}{ll} a & b \\ c & d \end{array}\right)$ in $\mathcal{M}_2(\mathbb{R})$ we consider the four points (possibly coinciding) $E = (d,-c)$, $F = (a,b)$, $G = (d,b)$ and $H = (a,-c)$.
In the case where $A = \left(\begin{array}{rr} 1 & 7 \\ -1 & 3 \end{array}\right)$, draw the circle and the quadrilateral $EHFG$.

For $A = \left(\begin{array}{ll} a & b \\ c & d \end{array}\right)$ in $\mathcal{M}_2(\mathbb{R})$ we consider the four points (possibly coinciding) $E = (d,-c)$, $F = (a,b)$, $G = (d,b)$ and $H = (a,-c)$.

In the case where $A = \left(\begin{array}{rr} 1 & 7 \\ -1 & 3 \end{array}\right)$, draw the circle and the quadrilateral $EHFG$.

Paper Questions

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