How do I use Gaussian elimination to solve a system of equations?
The goals of Gaussian elimination are to get
Then you can use back substitution to solve for one variable at a time.
Use Gaussian elimination to solve the following system of equations.
Set up an augmented matrix of the form.
Goal 1. Get a 1 in the upper left hand corner.
Goal 2a: Get a zero under the 1 in the first column.
Multiply Row 1 by
Add the result to Row 2 and place the result in Row 2.
We signify the operations as
Goal 2b: Get another zero in the first column.
To do this, we need the operation
Goal 2c. Get the remaining zero.
Multiply Row 2 by
Now use the operation
Multiply the third row by
Goal 3. Use back substitution to get the values of
Goal 3a. Calculate
Goal 3b. Calculate
Goal 3c. Calculate x.
The solution is