Matrix row reduction tutorial with infinite solutions

[mr_coffee]

Hello everyone, Anyone know any good tutorials that can explain to me how i can perform the following:
http://img499.imageshack.us/img499/9744/lastscan1jb.jpg
I know the basic jist of it, like all 000's in a row means infite, and that's about it

 

[EnumaElish]

Start with the Ax part. What does Ax mean, can you describe?

 

[TD]

I know the basic jist of it, like all 000's in a row means infite, and that's about it

Can you find a link with the determinant of the coefficient matrix?

 

[mr_coffee]

Well A is a matrix and x = <x,y,z> if its a 3x3; when b is the value of the matrix. TD, i found lots of homework problems but no solutions :(

 

[TD]

Have you seen the concept 'rank'? If the rank of the coefficient matrix is equal to the rank of the augemented matrix, then the system Ax = B has solutions.

Link with the determinant: if det(A) = 0 and A is an n x n matrix, then rank(A) < n, or: A is a singular matrix. If det(A) =! 0, then A is a regular matrix and its rank is n.