Which of the following options are correct?

Posted on 2016-02-29 19:04:00 in Math by RIDA

A.If the equation Ax = b is inconsistent, then b is not in the set spanned by the columns of A. 
B.If A is an m imes n matrix and if the equation Ax = b is inconsistent for some b in |R^m, then A cannot have a pivot position in every row. 
C.A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax = b has at least one solution. 
D.If the augmented matrix [ A b ] has a pivot position in every row, then the equation Ax = b is inconsistent. 
E.The equation Ax = b is referred to as a vector equation. 
F.The solution set of a linear system whose augmented matrix is [ a_1 a_2 a_3 b ] is the same as the solution set of Ax = b, if A = [ a_1 a_2 a_3 ].

Update: I know that A, E and F are correct but what about B, C and D. Are any of them correct? If so, which ones?

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