Solving Simultaneous Equations Using Row Reduction Operations on The Augmented Matrix

We can solve a sytem of linear simultaneous equations by forming the augemented matrix and using elementary row oprations to reduce to ipper triangular form. The solutions can then be found by back sunstitution.

Example: Solve the system of equations

2x-3y+5z=17

x-2y-3z=-3

3x+y+z=18

The augmented matrix is

We can interchange rows 1 and 2, to make the entry in the upper left hand corver 1.

Subtract twice the first row from the second row, and three times the first row from the second row.

Subtract seven times the second row from the third row.

From the third eow,

From the second row,

From the first row,