A system with n equations and n-2 variables in matrix form will
have n rows and n-2 cloumns. It is possible that every row is some
multiple of the pivot row. In that case, by reduction, it would be
a matrix with only one row, called the pivot row, and rest of the
rows would be reduced to all zeros. Such a matrix would be matrix
of rank one. It willl hve only one pivot column. This means that
there would be only one basis vector of the matrix, signifying that
solution set would be the span of a single vector.
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