grandes-ecoles 2016 QI.B.2

grandes-ecoles · France · centrale-maths1__psi Matrices Structured Matrix Characterization
Prove that $\mathcal{X}_2' = \mathcal{X}_2 \cap \mathrm{GL}_2(\mathbb{R})$ generates the vector space $\mathcal{M}_2$. For $n \geqslant 2$, does $\mathcal{X}_n'$ generate the vector space $\mathcal{M}_n(\mathbb{R})$? 
Prove that $\mathcal{X}_2' = \mathcal{X}_2 \cap \mathrm{GL}_2(\mathbb{R})$ generates the vector space $\mathcal{M}_2$. For $n \geqslant 2$, does $\mathcal{X}_n'$ generate the vector space $\mathcal{M}_n(\mathbb{R})$?
Paper Questions
QI.A.1 QI.A.2 QI.A.3 QI.A.4 QI.B.1 QI.B.2 QII.A.1 QII.A.2 QII.A.3 QII.B.1 QII.B.2 QII.B.3 QII.B.4 QIII.A.1 QIII.A.2 QIII.A.3 QIII.B.1 QIII.B.2 QIII.B.3 QIII.B.4 QIII.C QIV.A.1 QIV.A.2 QIV.A.3 QIV.A.4 QIV.A.5 QIV.A.6 QIV.A.7 QIV.B.1 QIV.B.2 QIV.B.3 QIV.B.4 QIV.B.5 QIV.B.6