Gaussian elimination (pivoting)

[Ray Vickson]

Or the notes in this picture is misleading ? It mentioned that the a11 or a22 is 0 , not when we pivot the a11 , the a21 and a31 is 0 ...

The note you post is 100% clear, so you must be reading it incorrectly. Remember: after swapping rows 1 and $i$, the old row $i$ becomes the new row 1, and vice-versa. The old $a_{i1}$ becomes the new $a_{11}$, and the old $a_{11}$ becomes the new $a_{i1}$.

 

[fonseh]

The note you post is 100% clear, so you must be reading it incorrectly. Remember: after swapping rows 1 and $i$, the old row $i$ becomes the new row 1, and vice-versa. The old $a_{i1}$ becomes the new $a_{11}$, and the old $a_{11}$ becomes the new $a_{i1}$.

It didnt mention about when after swapping row , the old a11 will become 0

 

[Ray Vickson]

It didnt mention about when after swapping row , the old a11 will become 0

No, you didn't, but the posted note DID, and that is all that counts here. You are trying to understand what the note is all about, and whether the note is correct. It is correct. (The note itself did not say that the old row i becomes the new row 1, etc., but it takes that as understood by the reader.)