The discussion revolves around the properties of a linear system of equations, specifically focusing on the implications of having leading 1's in the reduced row-echelon form of an augmented matrix. Participants are examining whether the presence of n leading 1's guarantees a unique solution.
The discussion is active, with participants exploring different interpretations of the definitions and implications of leading 1's in the context of the problem. There is no clear consensus, but various perspectives are being shared, including potential typographical errors in the source material.
Some participants note that the book they are referencing does not clearly delineate the augmented matrix, which may contribute to the confusion regarding the definition of leading 1's. This lack of clarity may be influencing their interpretations of the problem.
Yes it is, but is this all your attempt to the solution?tgt said:The Attempt at a Solution
True to me but is it?
kof9595995 said:Yes it is, but is this all your attempt to the solution?
kof9595995 said:Em...unless 1's in the augmented part can be called "leading 1",then the matrix can be like this:
1 0 2
0 0 1
But I have a very vague memory that the 1 in augmented part(1 in second row) can't be called "leading 1",but you should check it out.
tgt said:But there is n leading 1's with n variables. Your example have 2 leading 1's in 3 variables.
The question does say n leading 1's in the reduced echelon matrix. The fact that its reduced echelon suggest that all columns have 0 elsewhere.
kof9595995 said:No, my example is an augmented matrix, the 3rd column is the right hand side of the equations.
kof9595995 said:Personally I don't think 1 in augmented part can not be called leading one, and with roam's confirmation, probably it's just a typo in the book.