1. A system for reducing memory traffic and power consumption in a processing environment by efficiently solving a consistent set of linear equations represented by AX=B, said system comprising: one or more memory modules, wherein said one or more memory modules store the matrices A and B; and one or more processor modules, wherein said one or more processor modules: a) transform the rows of augmented matrix [A|B] to form [A′|B′], such that the rows of A′ are zero, effectively zero, or part of an orthonormal set, and form one or more solution features, including at least one of: i) a particular solution formed as (A′)*B′, and ii) a null space projection operator formed as I n −(A′)*A′; b) transform the rows of augmented matrix [A|I m ] to form [A′|M], such that the rows of A′ are zero, effectively zero, or part of an orthonormal set, and form one or more solution features, including at least one of: i) a generalized inverse G formed as (A*)M, ii) a particular solution formed as (A′)*MB or GB, and iii) a null space projection operator formed as I n −(A′)*A′ or I n −GA; or c) transform the rows of augmented matrix [A|B|I m ] to form [A′|B′|M], such that the rows of A′ are zero, effectively zero, or part of an orthonormal set; and form one or more solution features, including at least one of: i) a generalized inverse G formed as (A′)*M, ii) a particular solution formed as (A′)*B′, (A′)*MB or GB, and iii) a null space projection operator formed as I n −(A′)*A′ or I n −GA.