we have a system of linear equations as such:
and i have to find the solution in and so i have no problem for i get the matrix
but the questions i have are as follows:
1. Can i use what i found for the augmented matrix and the discussion by parameter a in to deduce ?
2. Or is there some other way i must reduce to row echelon form for and then have the discussion for parameter a?
3. If i had an 3x3 or 4x4 system to solve over a low prime and (eg 5 and 7) how would i go about doing it with the matrix gauss elimination?could i use the same augmented matrix and reduce it to row echelon over and then use that augmented matrix for the rest like above or not?
4. If i recall correctly there was a theorem about the rank of the original matrix and augmented that says something about the number of solutions but i do not recall how that would help me find solutions just eliminate the a's where there is none?