grandes-ecoles 2015 QV.C

grandes-ecoles · France · centrale-maths1__pc Matrices Eigenvalue and Characteristic Polynomial Analysis

In this part $E$ is a real vector space of dimension $n$ equipped with a basis $\mathcal{B} = (\varepsilon_i)_{1 \leqslant i \leqslant n}$. We consider an endomorphism $f$ of $E$ and we denote by $A$ its matrix in the basis $\mathcal{B}$.
Determine thus the stable plane(s) of $f$ when $n = 3$ and $A$ is the matrix $A = \begin{pmatrix} 1 & -4 & 0 \\ 1 & -2 & -1 \\ 1 & 1 & 0 \end{pmatrix}$ considered in IV.F.

In this part $E$ is a real vector space of dimension $n$ equipped with a basis $\mathcal{B} = (\varepsilon_i)_{1 \leqslant i \leqslant n}$. We consider an endomorphism $f$ of $E$ and we denote by $A$ its matrix in the basis $\mathcal{B}$.

Determine thus the stable plane(s) of $f$ when $n = 3$ and $A$ is the matrix $A = \begin{pmatrix} 1 & -4 & 0 \\ 1 & -2 & -1 \\ 1 & 1 & 0 \end{pmatrix}$ considered in IV.F.

Paper Questions

QI.A QI.B QI.C QI.D QII.A QII.B QIII.A QIII.B QIV.A QIV.B QIV.C QIV.D QIV.E QIV.F QV.A QV.B QV.C QV.D