There appears to be some conflict in terms of what the RREF(Row Reduced Echelon Form) of a matrix actually is.
Following are two different forms, both of which are commonly referred to as RREF:
|* * * *|
|0 * * *|
|0 0 * *|
Where * is a number.
This is what I was taught to refer to as RREF, however someone recently informed me that this form is actually called Row Reduced Form (thanks 10998521
It is simple to stop here, as simple division will give you the result for the bottom row, the inserting that result into the row above and solving will give you the solution for the second row, and so on (this is known as back substitution
) (essentially, it assumes that it is easier to do simple algebra than to work with elementary row operations
|1 0 0 *|
|0 1 0 *|
|0 0 1 *|
Where * is a number. This is what I was taught to refer to as Gauss
-Jordan form, but it is also
commonly referred to as RREF. It may not always be possible to achieve this form, but it is easier to read, as the solutions for each row are directly written in it.
On a side note, the echelon in RREF refers to the triangle shape that can be drawn around the zeroes in the corners.