Linear Algebra: use elem. row ops to convert A into B

[leo255]

Homework Statement

Show that the given matrices are row equivalent and find a sequence of elementary row ops that will convert A into B.

a =
2 0 -1
1 1 0
-1 1 1

b =
3 1 -1
3 5 1
2 2 0

Homework Equations

The Attempt at a Solution

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I apologize in advance, as I'm not sure how to make these matrices look good (will need to look up LATEX, so I can present my matrices better).

The elementary row ops that I chose to do were as follows:

R2 + R1 --> R1
R2 <---> R3
R3 + R2 -->R2
R1 + R2 --> R2
2R3 --> R3
R3 + R2 --> R2

This gave me the following matrix, which is not the answer, but is my best try:

a =
3 1 -1
5 5 0
2 2 1

 

[Svein]

R2 + R1 --> R1
R2 <---> R3
R3 + R2 -->R2
R1 + R2 --> R2
2R3 --> R3
R3 + R2 --> R2

Close..
R2 + R1 →R1 OK
4*R2 + R3→R2
Now do the third row...