Row Reduction Method in solving system of equation

[honest_denverco09]

We know that we can use the matrix inverse to solve the system of equations, but there are many ways to do so, in this topic, i would like to discuss about "ROW REDUCTION METHOD" in solving the system of equations, which is thought the most difficult to use for me! .

The most difficult part is that how can we use the row operations to converse the "augmented matrix" into the "solution matrix" that contains "identity matrix" and our "solution matrix").

For example we have the system of equation is : 2x + y = 5 and 5x + 3y = 13. How can we change to solution matrix ?

[stapel_eliz]

To learn about row operations, try here.

It should be noted that solving a system by using row operations on the augmented matrix is just a simpler (easier to work with, anyway) method of doing row operations to solve a system of equations. Just as, in that case, you would want to get down to "x=(something), y=(something else)", so also you want now to get a matrix with the identity matrix on the left-hand "side", as this represents "x=, y=".