The textit{QIF}  (Quadrant Interlocking Factorization) method of Evans and Hatzopoulos solves linear equation systems using textit{WZ}  factorization. The  WZ factorization can be faster than the textit{LU} factorization  because,  it performs the simultaneous evaluation of two columns or two rows. Here, we present a  method for computing the real and integer textit{WZ} and  textit{ZW} factorizations by using the null space generators of some special nested submatrices of a matrix textit{A}.

Keywords: Linear systems, Quadrant interlocking factorization, WZ factorization, ZW factorization, Null space generator.

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