grandes-ecoles 2018 Q4

grandes-ecoles · France · x-ens-maths1__mp Matrices Determinant and Rank Computation

We consider three strictly positive integers $n , p$ and $k$ such that $\mathscr { M } _ { n , p } ^ { k } ( \mathbb { R } )$ is non-empty. Let $A$ be a matrix of $\mathscr { M } _ { n , p } ^ { k } ( \mathbb { R } )$.
Show that $k \leqslant \min ( n , p )$ and that for all $\lambda \in \mathbb { R } ^ { * } , \lambda A \in \mathscr { M } _ { n , p } ^ { k } ( \mathbb { R } )$.

We consider three strictly positive integers $n , p$ and $k$ such that $\mathscr { M } _ { n , p } ^ { k } ( \mathbb { R } )$ is non-empty. Let $A$ be a matrix of $\mathscr { M } _ { n , p } ^ { k } ( \mathbb { R } )$.

Show that $k \leqslant \min ( n , p )$ and that for all $\lambda \in \mathbb { R } ^ { * } , \lambda A \in \mathscr { M } _ { n , p } ^ { k } ( \mathbb { R } )$.

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