A Cramer rule for finding the solution of a class of singular equations (Q1119713)

Let A be an \(n\times n\) complex matrix and let k be the least nonnegative integer such that rank \(A^ k=rank A^{k+1}\). If b is in the range of \(A^ k\), then there is a unique x in the range of \(A^ k\) such that \(Ax=b\). The author obtains a Cramer's rule type result for finding this solution. The result reduces to the usual Cramer's rule for nonsingular A.