I've consulted a few other sources for a possible answer to this question, but I am still in need of a formulaic answer. One such answer read as this:
"For every column b of B, you get a column solution to Ax=b.
Assemble all of those columns x into X (in the same order that you got them from b in B). For example, the third column of X will be a solution to Ax=b, where b is the third column of B."
How would I show this in terms of mathematical formulas? Or is that thinking the wrong way?