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# 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.
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• Description: find two matrices whose product is a given matrix. interactive exercises, online calculators and plotters, mathematical recreation and games, Pôle Formation CFAI-CENTRE
• Keywords: CFAI,interactive math, server side interactivity, algebra, linear_algebra, matrix, rank, vectors