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Rankmult

Rankmult
--- Introduction ---

Rankmult
is an exercise on the multiplication of matrices:
one knows that if $C$ is a matrix of size $m\times n$ and
of rank $r$, then there exist two matrices $A$ and $B$, of sizes
$m\times r$ and $r\times n$ respectively, such that $C=AB$.
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. exercises interactifs, calcul et tracé de graphes en ligne

Keywords: interactive mathematics, interactive math, server side interactivity, algebra, linear_algebra, matrix, rank, vectors