Wehave seen thatthe Gauss-Jordan elimination is the most basic technique for solving a system Ax = b of linear equations and it can be written in matrix notation as an LDU factorization. Moreover, the questions of the existence or the uniqueness of the solution are much easier to answer after the Gauss-Jordan elimination. In particular, if det A ≠ 0, x = 0 is the unique solution Ax = O. In general, the set of solutions of Ax = 0 has a kind of mathematical structure, called a vector space,and with this concept one can characterize the uniqueness of the solution of a system Ax = b of linear equations in a more systematic way.
KeywordsVector Space Column Vector Null Space Free Variable Scalar Multiplication
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