Forward elimination:
In forward elimination, we want to obtain a 0 in the a_{21} position. To accomplish this, we can alter the second line in the matrix by subtracting from it 2 * the first row.
In this way we would write this ERO as:
Now, placing it back in the matrix equation form:
It says that the second equation is now -2_{x2} = 2 therefore x_{2} = -1. Now put it into the first equation:
x_{1} + 2(-1) = 2, and hence x_{1} = 4.
This is known as the back-substitution.