I do not get the difference between Gauss and Gauss-Jordan with regards to solving linear system. In the Gauss method, you start by forward reduction and then move on to back substitution. In Gauss-Jordan, you start by forward reduction but then backward elimination. However, isn't back-substitution the same as backward elimination? I mean you are in some sense performing elementary row operations to substitute into other equations, right?
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The Gauss method turns the matrix to upper triangular, then you solve the triangular system.
The Gauss-Jordan method turns the matrix directly to unit instead.
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"then you solve the triangular system" - but don't you solve it by using elementary row operations? – That Guy Apr 20 '20 at 15:27
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@Dip: and then ? – Apr 20 '20 at 15:32
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The main difference between Gauss and Gauss Jordan is that the Gauss-Jordan method consists of eliminating all the terms of the coefficient matrix until leaving an identity matrix, which results in the column of independent terms containing the solutions of the system. On the other hand, in the Gaussian method, only the diagonal below is eliminated and then the remaining terms are used to make a substitution and find the solutions.
Katia Alonzo
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