PS1: What do you mean by "matrix algebra representation" of factor analysis?

Could you give me a bit more information about what you mean by expressing it in matrix algebra "representation." Do you want the commonly used matrix labels (e.g. L = V'RV) - and a succession of the steps needed to get through it? Or do you want the steps, but with the actual matrices and their values?

The task here is to communicate that you understand not only how to interpret your FA results (which is the motivation behind the rest of the problem set), but also the analytical process giving rise to these results. To best communicate this understanding, show the various steps of factor analysis estimation, and when most appropriate (but not overly inconvenient), include, say, a description of what each matrix represents and/or how it is estimated, and even the first couple entries if that is something that is easily generated (or found in your statistical output). For example, when it comes to statistical values (e.g., factor loadings) that you may interpret, show me where those actually fit in a matrix along the steps of estimation....and maybe say something like (the first couple rows/columns/diagonal values are .87 and .62). Don't go into things that are too complicated, though -- something like "the steps required to invert matrix D are" is probably unnecessary.