grandes-ecoles 2021 Q12

grandes-ecoles · France · centrale-maths1__psi Matrices Linear System and Inverse Existence

Let $M \in M _ { n } ( \mathbb { R } )$, all of whose coefficients are non-negative. Show that $M$ is a stochastic matrix if and only if $$M \left( \begin{array} { c } 1 \\ \vdots \\ 1 \end{array} \right) = \left( \begin{array} { c } 1 \\ \vdots \\ 1 \end{array} \right) .$$

Let $M \in M _ { n } ( \mathbb { R } )$, all of whose coefficients are non-negative. Show that $M$ is a stochastic matrix if and only if
$$M \left( \begin{array} { c } 1 \\ \vdots \\ 1 \end{array} \right) = \left( \begin{array} { c } 1 \\ \vdots \\ 1 \end{array} \right) .$$

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