The rank of a matrix plays a very important role in linear
algebra. It conditions the linear dependence of vectors, or the existence
of non-zero solution of a homogeneous linear system.
This exercise gives you a matrix (presented under
different forms: vectors, linear system), some elements of which
are missing. You have to find the values of the missing elements,
such that the matrix has a rank smaller than its size.
If you are expert, you may choose parameters of the exercise in a
This exercise originates from an idea of Frédéric Pham.
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