 In this case, the matrix formed by the vectors is
We may write a linear combination of the columns as
We are interested in whether "A"Λ = 0 for some nonzero vector Λ.This depends on the determinant of "A", which is
Since the determinant is non-zero, the vectors (1, 1) and (−3, 2) are linearly independent.Otherwise, suppose we have "m" vectors of "n" coordinates, with "m" 1...,"i""m"〉 is any list of "m" rows, then the equation must be true for those rows.