Let's say you're a big, BIG fan of Barry Manilow. Don't worry, we won't say it to anyone else. You have a collection that consists of 8 vinyl records, 6 eight-track tapes, 7 cassettes, and 3 CDs. You want to place the data about your collection into a matrix. What would that matrix look like?

The matrix looks like this:

...because we're just listing one thing: the type of recording.

Let's say we want to be more detailed about our Manilow Mania. We want to list in a matrix how many of each "Greatest Hits" (1978) and "Ultimate Manilow" (2004) albums we have. Of the 8 records, there are 5 "Greatest Hits" and 3 "Ultimate Manilow." For eight-tracks it's 4 and 2, for cassettes it's 2 and 5, and for CDs it's 1 and 2.

Here is what our matrix looks like:

Finally, let's suppose we bought some of each of these works on eBay and some at Julio's Retro Wonderland, and for some reason, this matters to us. For sanity's sake, let's use this shorthand: G = Greatest Hits, U =Ultimate Manilow, E = eBay, and J = Julio's place. Here are our lists:

Matrix E (our eBay purchases)

Vinyl records: 3G, 3U
8 tracks: 1G, 1U
Cassettes: 2G, 3U
CDs: 1G, 0U

Matrix J (our Julio's bargains)

Vinyl records: 2G, 0U
8 tracks: 3G, 1U
Cassettes: 0G, 2U
CDs: 0G, 2U

What does matrix E look like? How about matrix J?