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--- Introduction ---
is an exercise on the multiplication of matrices:
one knows that if is a matrix of size and
of rank , then there exist two matrices and , of sizes
and respectively, such that .
It's normal if you don't know a formula allowing you to ``compute''
and from , as the solution
is not unique (in fact there are infinitely many solutions for each ).
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.