Proving the Relationship Between Augmented Matrices and Reduced Row Echelon Form

[BK201]

Hi,

i have just started with learning linear algebra ,so please bear with me. It seems like a quite simple question:

Let [A b] an augmented matrix. Prove that if its reduced row echelon form (rref) is [R c] ,then R is the rref of A.

 

[HallsofIvy]

What is the defintion of "reduce row echelon form"?

 

[BK201]

First ,thanks for replying.

rref is the simplest and most suitable form for Gaussian Elimination obtained by applying elementary row operations.(interchange ,scaling ,or row addition)

Following are requirements :
1.Every nonzero row lies above each zero row.
2.The leading entry of a nonzero row lies in a column to the right of the column containing the leading entry of any preceding row.
3.If a column contains the leading entry of some row ,then all the other entries in that column are zero.
4.The leading entry of each nonzero row is 1.

ex:

1 0 * * 0 0 *
0 1 * * 0 0 *
0 0 0 0 1 0 *
0 0 0 0 0 1 *
0 0 0 0 0 0 0 (* represents arbitrary real number)

A row with no other entry except zero is referred to zero row ,vice versa.