## Using Augmented Matrices

Augmented Matrices is the easiest method to solve a system of equation as long as you have a calculator in your hand. Also, it works with any kind of system 2 variable 3 variable or even 4 variable. This method is very similar to the Matrix Inverse Method in the beginning. You have to convert the equations into standard form, this isolates the variables to one side. Again, you have to make a 2x2 or 3x3 matrix depending on the # of equations. Next, you plug in the coefficients into the 3x3 matrix, just like the Matrix Inverse Method, however don't draw a bracket on the right side of the matrix, because we have to make an augmented matrix. All you need to do is to add a straight line on the right side, but you need to keep the bracket on the left side. To the right of the straight line you need to plug in the products of the 3 equations, just like in the Matrix 'B' in the Matrix inverse method. The product of the first equation on the top component, the product of the 2nd component in the 2nd component and so on... Now you can draw the bracket onto the matrix. Next, you have to plug the matrix into the calculator. You may have realized that the calculator can't make augmented matrices, but it doesn't matter if there is not a line in the middle, plug in the matrix as a 3x4 matrix. Then you need to find the rref function which stands for Reduced-Row Echelon Form. This form basically just does a bunch of row operations for you and spits out the last column of number. The rref function makes the 3x3 matrix that you start out with into the 3x3 identity matrix. Thus, the numbers in the augmented column is the values of x,y,z respectively.