Solving two linear systems Ax=b with same coefficients

Example of solving two 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 two linear systems 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] and use matrix row operations to convert the 3x3 matrix into the RREF. You can easily determine the answers once you convert them to the RREF.

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

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

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