What is the meaning of the notation [A|B] in Linear Algebra. I am going through Linear Algebra right now, we are using the book Elementary Linear Algebra by Andrilli. In one of the theorems he uses this notation without really introducing it. Here is the theorem:
Theorem 2.3 Let AX=B be a system of linear equations. If [C|D] is row equivalent to [A|B], then the system CX=D is equivalent to AX=B.
I just don't know how to read the [C|D] notation there. I want to say C divides D because that's the symbol for integer division, but I know that's not right.
Thanks!
 A: 
Let AX=B be a system of linear equations. If [C|D] is
  row equivalent to [A|B], then the system CX=D is
  equivalent to AX=B.

$[A\mid B]$ is just a $1\times 2$ matrix consisting of two matrix blocks $A$ and $B$ as first and second column entry.
So $\mid$ acts as layout separator not as division operator.
You could express the same as 

.. If $C$ is row equivalent to $A$ and $D$ is row equivalent to $B$, then
  ..

but the aggregation via blocks allows more compact
statements.
Example:
$$
A X = B
$$
with
$$
A =
\begin{bmatrix}
1 & 2 \\
3 & 4
\end{bmatrix}
\quad
X =
\begin{bmatrix}
x_{11} & x_{12} \\
x_{21} & x_{22}
\end{bmatrix}
\quad
B =
\begin{bmatrix}
1 & 0 \\
4 & -1
\end{bmatrix}
$$
then
$$
[A \mid B] =
\left[
\begin{array}{rr|rr}
1 & 2 & 1 & 0 \\
3 & 4 & 4 & -1
\end{array}
\right]
$$
where I added the vertical line just for visual separation.
A: In this context, the $[\mathbf{A}|\mathbf{B}]$ notation signifies an "augmented matrix" associated with a system of linear equations. Your textbook probably has a definition of "augmented matrix". Try looking up this term in the index.
The concept is simple enough: $[\mathbf{A}|\mathbf{B}]$ is just the matrix $\mathbf{A}$, but with the vector $\mathbf{B}$ glued on as an extra column on the right. So, if $\mathbf{A}$ has $n$ columns, then $[\mathbf{A}|\mathbf{B}]$ will have $n+1$ columns.
More generally, $[\mathbf{A}|\mathbf{B}]$ denotes the matrix formed by gluing together two matrices $\mathbf{A}$ and $\mathbf{B}$.
