16.5 Gaussian Elimination

  • Row Echelon Form • Gaussian Elimination • Number of Possible Solutions • Consistent and Inconsistent Systems

We now show a general method that can be used to solve a system of linear equations. The procedure used in this method is similar to that used in finding the inverse of a matrix in Section 16.3. It is known as Gaussian elimination, and as noted in the chapter introduction, it was developed in the early 1800s by Karl Gauss. Today, it is commonly used in computer programs for the solutions of systems of linear equations.

When using this method, we use certain row operations to convert the system of equations to row echelon form. Then the solution can be found by substituting back into the equations from the ...

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