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 matrix C, randomly generated, which is . 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   matrices   linear algebra  

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