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A solution of linear systems of equations Ax=b and Ax=0 is a vital part ofmany computational packages. This paper presents a novel formulation based onthe projective extension of the Euclidean space using the outer product(extended cross-product). This approach enables to solve the both cases, i.e.Ax=b and Ax=0. The proposed approach leads actually to an analytical solutionof linear systems in the form on which the other vector operation can beapplied before using the numerical evaluation.  This contribution also proposes a new approach to the conditionalityestimation of matrices applicable to non-squared matrices. It splits theconditionality to structural conditionality showing matrix property if nearlyunlimited precision is used, numerical issue which depends on numericalrepresentation with respect to the right-hand side influence, if given.

Solution of Linear Systems of Equations Ax=b and Ax=0 using Unifying  Approach with Geometric Algebra: Outer Product Application and Angular  Conditionality