Well, what have you done on this? You might think about how the last column of A relates to the first n columns in light of the fact that " A is the augmented m x (n + 1) matrix of a system of m linear equations
with n unknowns".
If we let A be the augmented m x (n + 1) matrix of a system of m linear equations
with n unknowns
Let B be the m x n matrix obtained from A by removing the last
column.
Let C be the matrix in row reduced form obtained from A by elementary
row operations.
Prove the the following statements are equivalent:
(i) The linear equations have no solutions
(ii) If ,......, are the columns of A, then is not a linear combination of
,......,
ok, since it is the augmented matrix then we can get a system of m linear equations, I'm not sure why exactly they are linear but we will use the fact that
A has m rows and each column of A will have c .... c we will make our linear equations but I think we can only achieve this if m=n?
these are my first thoughts