grandes-ecoles 2010 QI.A.2

grandes-ecoles · France · centrale-maths2__mp Proof Proof of Set Membership, Containment, or Structural Property
If $A$ is a subset of $E$, we denote $A^{\perp\varphi} = \{ x \in E \mid \forall a \in A,\ \varphi(x,a) = 0 \}$. Show that $A^{\perp\varphi}$ is a vector subspace of $E$. 
If $A$ is a subset of $E$, we denote $A^{\perp\varphi} = \{ x \in E \mid \forall a \in A,\ \varphi(x,a) = 0 \}$. Show that $A^{\perp\varphi}$ is a vector subspace of $E$.
Paper Questions
QI.A.1 QI.A.2 QI.A.3 QI.A.4 QI.B.1 QI.B.2 QI.B.3 QII.A.1 QII.A.2 QII.A.3 QII.A.4 QII.B.1 QII.B.2 QII.B.3 QII.B.4 QII.C.1 QII.C.2 QII.C.3 QII.C.4 QII.C.5 QIII.A.1 QIII.A.2 QIII.B.1 QIII.B.2 QIII.B.3 QIV.A.1 QIV.A.2 QIV.A.3 QIV.A.4 QIV.B.1 QIV.B.2 QIV.B.3 QIV.B.4