




2 x 
+3 y 
+7 z 
= 2 
x 
 y 
 z 
= 1 
x 

+ z 
= 1 
A = 

V = 

STANDARD METHOD: 
GAUSSIAN ELIMINATION: 

1. Solve first equation for x by dividing it by two and moving y and z terms to other side:

1.Divide first row of A and V by 2:


2. Substitute in other equations for x:

2. Subtract first row of A and V from each other row of A and V:


3. Solve second equation for y:

3. Divide second row by 5/2:


4. Substitute for y in third:

4. Add 3/2 of second row to third:


5. Multiply third equation by 5:

5. Multiply third row by 5:


Current form of equations:

Current A and V:


6. Substitute for z in first two equations:

6. Subtract 7/2 of third row from first and 9/5 of it from second row:


7. Substitute for y in the first equation:

7. Subtract 3/2 of 2nd row from 1st:

You see, if you follow this example, that solving equations by systematically eliminating variables, and using Gaussian elimination to change a matrix into the identity matrix are essentially the same thing.