Sage Essentials 3.a01

Last Updated 10/28/2022

Sage Essentials
Section 7: Matrix Manipulations

Gauss-Jordan Eliminations (GJE)

To perform GJE, the system is first encoded into an augmented matrix A. Then the system can be solved by the rref command.

Solve the system ${\begin{matrix} x + y + z = 4 \\ 2 x + 2 y + 5 z = 11 \\ 4 x + 6 y + 8 z = 24 \end{matrix}$ by GJE.

The solution is encoded in the last column of the matrix. In this case, it is ${\begin{matrix} x = 1 \\ y = 2 \\ z = 1 \end{matrix}$ .

Try this!

Solve the system ${\begin{matrix} x - 2 y + 3 z = 9 \\ - x + 3 y = - 4 \\ 2 x - 5 y + 5 z = 17 \end{matrix}$ by GJE.