System of linear equations Common form of system of linear equations is A*X = B, X is unknown. But how to find A, if X and B are known?
A is MxN matrix, X is column vector(N), B is column vector(M)   

Do it row by row. Row $k$ in $A$ multiplied by the column vector $X$ equals the $k$th entry in the vector $B$. This is a single equation for the $N$ entries in that row of $A$ (so unless $X$ is zero, you get an $(N-1)$-parameter set of solutions for each row).
