Enter your matrices line by line, separating the elements by commas.!set lang_exists=yes Enter your matrices line by line, separating the elements by commas.!set lang_exists=yes Enter your matrices line by line, separating the elements by commas.!set lang_exists=yes !! used as default html header if there is none in the selected theme. Rankmult

# Rankmult --- Introduction ---

Rankmult is an exercise on the multiplication of matrices: one knows that if $C$ is a matrix of size $m×n$ and of rank $r$, then there exist two matrices $A$ and $B$, of sizes $m×r$ and $r×n$ respectively, such that $C=AB$.
The server will therefore give you such a randomly generated matrix $C$ . And you are asked to find the matrices $A$ and $B$.
Remark. It's normal if you don't know a formula allowing you to compute'' $A$ and $B$ from $C$, as the solution is not unique (in fact there are infinitely many solutions for each $C$). What you need is a good dose of reflexion. Try first the case where rank=1, which is rather easy. For bigger ranks, computations of linear combinations of vectors will be necessary in general.

Other exercises on: Rank   Matrix   Linear algebra

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• Description: find two matrices whose product is a given matrix. serveur web interactif avec des cours en ligne, des exercices interactifs en sciences et langues pour l'enseigment primaire, secondaire et universitaire, des calculatrices et traceurs en ligne
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