The two columns of the matrix and the column are regarded as vectors in a plane.
Difficulty arises when the two column vectors of the matrix point in the same direction.
The same thing may be said about the general case. If is an matrix, then its columns are required to span an n -dimensional space. In particular, the n -dimensional parallelopiped with edges given by the columns of should not have a zero volume. Such a volume is given by the determinant of . This set always has the solution which is often called the trivial solution.