grandes-ecoles 2016 QIII.B.3

grandes-ecoles · France · centrale-maths1__mp 3x3 Matrices Matrix Algebraic Properties and Abstract Reasoning

Let $A$ be a primitive matrix and $m \in \mathbb{N}^*$ such that $A^m > 0$. Show that $\forall p \geqslant m, A^p > 0$. You may note, by justifying it, that none of the columns $c_1, c_2, \ldots, c_n$ of $A$ is zero.

Let $A$ be a primitive matrix and $m \in \mathbb{N}^*$ such that $A^m > 0$. Show that $\forall p \geqslant m, A^p > 0$. You may note, by justifying it, that none of the columns $c_1, c_2, \ldots, c_n$ of $A$ is zero.

Paper Questions

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