Solving system of linear equations
system of linear equations -> Ax=b
(m by n coefficient matrix A)
-> [A | b]
(the augmented matrix)
----------------------------------------> (three possible outcomes)
row elementary operations ,
column permutation
,
dropping redundant rows
0| 0 ---> 0=0
(every x is a solution)
0 | 1 ---> 0 =1
(there are no solutions)
y
T
z
T
=
-------- ----> y=-Cz+d
(variables in z, if any, take arbitrary values; k <= m)
1
k
C | d