Example of solving three linear systems Ax=b (nonhomogeneous systems) with the same coefficients.

This Linear Algebra video tutorial provides a basic introduction into the Gauss-Jordan elimination which is a process that involves elementary row operations with 3x3 matrices which allows you to solve a system of linear equations with 3 variables (x, y, z).

❖ Solve a linear system Ax=b1 and Ax=b2 by using a Reduced Row Echelon Form (RREF).
(Sometimes, they called this method as Gauss-Jordan elimination ( or Gauss-Jordan reduction) method).

❖ To solve a linear system of equations by Gauss Jordan elimination, we have to put it in RREF.

So, you need to convert the system of linear equations into an augmented matrix [ A | b1 | b2 | b3 ] and use matrix row operations to convert the 3x3 matrix into the RREF. You can easily determine the answers once you convert to the RREF.

❖ We have solved the two systems (Ax=b1, Ax=b2, and Ax=b3) in the following way:

[ A | b1 | b2 | b3 ] to [ REFF | c1 | c2 | c3 ]
(b1, b2 and b3 vectors) changed to (c1, c2 and c3 vector) because we have done RREF for the augmented matrix [ A | b1 | b2 | b3 ].

0:00 Introduction & solve system C
3:58 The solution for system C
4:23 ❖ Conclusion

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