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!
Best Answer
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 $\mathbf{B}$.