Row Reduced Echelon Form (LINEAR ALGEBRA)?

When you are using an augmented matrix to represent a system of equations, then converting to reduced row echelon form is EXACTLY THE SAME as solving the equations by elimination - it's just a shorthand so you don't have to write out all the variables on every line. Think about how you would solve the following: x + y + z = 6 x + 2y + 3z = 14 x + y - z = 0 you'd probably start by subtracting the third equation from the first, leaving 0x + 0y + 2z = 6 z = 3 in matrix form, the system is represented by the augmented matrix 1 1 1 | 6 1 2 3 | 14 1 1 -1| 0 subtracting the bottom row from the top leaves 0 0 2 | 6 and dividing that by 2 leaves 0 0 1 | 3 You see how this is the same as manipulating equations with variables? The goal of solving systems of equations is to eliminate as many variables as possible.

The goal of reduced row echelon form is to turn as much of the matrix to 0 as possible. Now, you could write a new set of equations.

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