Which of the following statements are true?

A.

Any linear combination of vectors can always be written in the form $Ax$ for a suitable matrix $A$ and vector $x$.

B.

The equation $Ax = b$ is consistent if the augmented matrix $[$ $A$ $b$ $]$ has a pivot position in every row.

C.

The equation $Ax = b$ is referred to as a vector equation.

D.

The first entry in the product $Ax$ is a sum of products.

E.

If the equation $Ax = b$ is inconsistent, then $b$ is not in the set spanned by the columns of $A$.

F.

If the columns of an $m \times n$ matrix

$A$ span ${\mathbb R}^m$, then the equation

$Ax = b$ is consistent for each $b$ in ${\mathbb R}^m$.